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Monday, 15.04.2024, 14:30 (WIAS-406)
Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Dr. Anthony Nouy, Ecole Centrale de Nantes, Frankreich:
Moment methods for some optimal transport problems and parameter-dependent equations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
Most optimal transport (OT) solvers are currently based on an approximation of underlying measures by discrete measures. Another route is to approximate moments of measures, when these are determinate. Here, we show that many common OT problems can be formulated as generalized moment problems [1]. These include the computation of Lp Wasserstein or Gromov-Wasserstein distances and the corresponding barycenters. For measures supported on compact semi-algebraic sets, a practical numerical approach then consists in truncating moment sequences up to a certain order, and using the polynomial sums-of-squares hierarchy. The approach is proved to converge. It allows to extract a posteriori relevant information on the measures, such as their supports that can be estimated using Christoffel-Darboux kernels. In a second part of this talk, we present how these moment methods can be used for the solution of parameter-dependent hyperbolic equations, by using weak formulations on measure-valued solutions [2]. These methods can be used to directly approximate the solution as a function of the parameter, or to construct reduced order models by interpolation in Wasserstein spaces.

These are joint works with Olga Mula and Clément Cardoen, Swann Marx and Nicolas Seguin.


References:

[1] O. Mula and A. Nouy. Moment-SoS methods for optimal transport problems, arXiv:2211.10742, 2022.

[2] C. Cardoen, S. Marx, A. Nouy, and N. Seguin. A moment approach for entropy solutions of parameter-dependent hyperbolic conservation laws, 2024.

Host
WIAS Berlin

Wednesday, 10.04.2024, 14:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
M.Sc. Tim Böhnlein, Technische Universität Darmstadt:
Bounded functional calculus and dynamical boundary conditions
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We consider divergence form operators with complex coefficients on an open subset of Euclidean space. Boundary conditions in the corresponding parabolic problem are dynamical, that is, the time derivative appears on the boundary. As a matter of fact, the elliptic operator and its semigroup act simultaneously in the interior and on (a part of) the boundary. We extrapolate the bounded functional calculus in the Lebesgue scale. In particular, this implies maximal regularity as a starting point to treat nonlinear equations. Our strategy relies on extending a contractivity criterion due to Nittka and a non-linear heat flow method popularized by Carbonaro--Dragičević. This is joint work with Moritz Egert and Joachim Rehberg.

Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 10.04.2024, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Heide Langhammer, WIAS Berlin:
A spatial coagulation process
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
In this talk we consider a spatial version of the Marcus-Lushnikov process. This is a Markov process where particles are equipped with a spatial location and a mass and undergo a series of coagulation events. In a coagulation event a pair of particles is merged and replaced by a new particle. The mass of the newly formed particle is the sum of the former two and its location is sampled according to a given distribution. The rate of a coagulation event depends on the location and masses of the particle pair via a coagulation kernel. For the non-spatial version of this model it is known that for certain kernels a gelation phase transition occurs, which describes the formation of one or several large particles after a finite time. In this talk we introduce a new approach for studying the coagulation process. We will provide a formula that connects the distribution of the particle configuration to a Poisson point process and show how this can be used to derive a large deviation principle. From this we gain new insights into the limiting behaviour of the process and obtain criteria for the gelation phase transition.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
April 10 – 12, 2024 (IVW)
Workshop/Konferenz: Leibniz MMS Days 2024
more ... Location
Leibniz-Institut für Verbundwerkstoffe GmbH Kaiserslautern

Host
Leibniz-Institut fuer Verbundwerkstoffe GmbH IVW
WIAS Berlin
Tuesday, 09.04.2024, 13:30 (Online Event)
Seminar Materialmodellierung
Cécile Daversin-Catty, Simula Research Laboratory, Norwegen:
Mixed-dimensional coupled finite elements in FEniCS(x) (online talk)
more ... Location
Online Event

Abstract
Mixed-dimensional partial differential equations (PDEs) are equations coupling fields defined over distinct domains that may differ in topological dimension. Such PDEs naturally arise in a wide range of fields including geology, bio-medicine, and fracture mechanics. Mixed-dimensional models are also used to impose non-standard conditions through Lagrange multipliers. Finite element discretizations of such PDEs involve nested meshes of possibly heterogeneous topological dimension. The assembly of such systems is non-standard and non-trivial, and requires the design of both generic high level software abstractions and lower level algorithms. The FEniCS project aims at automating the numerical solution of PDE-based models using finite element methods. A core feature is a high-level domain-specific language for finite element spaces and variational forms, close to mathematical syntax. Lately, FEniCS gave way to its successor FEniCSx, including major improvements over the legacy library. An automated framework was developed in core FEniCS legacy libraries to address the challenges characterizing mixed-dimensional problems. These concepts were recently ported to FEniCSx, taking advantage of the underlying upgrades in the library features and design. This talk gives an overview of the abstractions and algorithms involved, and their implementation in the FEniCS project core libraries. The introduced features are illustrated by concrete applications in biomedicine.

Further Informations
Link on request (dirk.peschka@wias-berlin.de).

Host
WIAS Berlin
Thursday, 04.04.2024, 16:00 (WIAS-ESH)
Forschungsseminar Mathematische Modelle der Photonik
Prof. Dmitry Turaev, Imperial College London, GB:
4-winged Lorenz attractors
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We show that bifurcations of periodic orbits with multipliers (-1,i,-i) can lead to the birth of pseudohyperbolic Lorenz-like attractors of three different types: one is a discrete analogue of the classical Lorenz attractor, and the other two are new:two- and four-winged Simo angels. These three attractors exist in an orientation-reversing, three-dimensional, quadratic Henon map. This implies the abundance of such attractors in a class of systems with homoclinic tangencies. Our analysis is based on the study of a normal form for this bifurcation, a slow-fast three-dimensional system of differential equations with a Z4-symmetry. The existence of the continuous-time counterparts of the pseudohyperbolic attractors is established for the normal form as a part of an extensive numerical analysis of its bifurcations. In particular, we establish that all three types of continuous-time pseudohyperbolic attractors are born out of a certain Z4-symmetric heteroclinic configurations with three saddles.

Further Informations
Forschungsseminar Mathematische Modelle der Photonik

Host
WIAS Berlin
Tuesday, 02.04.2024, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Vaios Laschos, WIAS Berlin:
Optimal transport meets rough paths
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Further Informations
Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Tuesday, 26.03.2024, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Emilio Ferrucci, University of Oxford, GB:
Constraint-based causal discovery in stochastic dynamical systems
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
Predicting real-world phenomena often requires an understanding of their causal relations, not just their statistical associations. I will begin this talk with a brief introduction to the field of causal inference in the classical case of structural causal models over directed acyclic graphs, and causal discovery for static variables. Introducing the temporal dimension results in several interesting complications which are not well handled by the classical framework. The main component of a constraint-based causal discovery procedure is a statistical hypothesis test of conditional independence (CI). We develop such a test for stochastic processes, by leveraging recent advances in signature kernels. Then, we develop constraint-based causal discovery algorithms for acyclic stochastic dynamical systems (allowing for loops) that leverage temporal information to recover the entire directed graph. Assuming faithfulness and a CI oracle, our algorithm is sound and complete. We demonstrate strictly superior performance of our proposed CI test compared to existing approaches on path-space when tested on synthetic data generated from SDEs, and discuss preliminary applications to finance. This talk is based on joint work with Georg Manten, Cecilia Casolo, Søren Wengel Mogensen, Cristopher Salvi and Niki Kilbertus: https://arxiv.org/abs/2402.18477.

Further Informations
Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Tuesday, 19.03.2024, 15:00 (WIAS-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Alexandra Suvorikova, WIAS Berlin:
Bernstein-type inequalities for unbounded martingales and empirical processes
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Further Informations
Hybrid event. Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
March 18, 2024 (WIAS-ESH)
Workshop/Konferenz: Women in Math - Introduction of the Iris Runge Postdoc Program
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin
March 11 – 15, 2024 (HUB-Mitte)
Workshop/Konferenz: Workshop on Optimal Transport from Theory to Applications Interfacing Dynamical Systems, Optimization, and Machine Learning
more ... Location
Humboldt-Universität zu Berlin, Dorotheenstr. 24, 10117 Berlin, Universitätsgebäude am Hegelplatz

Host
WIAS Berlin
March 6 – 7, 2024 (Erwin-Schroedinger-Zentrum)
Workshop/Konferenz: WIAS Days 2024
more ... Location
Erwin-Schrödinger Zentrum Adlershof , Rudower Chaussee 26, 12489 Berlin.

Host
WIAS Berlin
Monday, 04.03.2024, 10:00 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. A.F.M. ter Elst, University of Auckland, Neuseeland:
The Dirichlet problem for elliptic equations without the maximum principle
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Thursday, 29.02.2024, 16:00 (WIAS-ESH)
Forschungsseminar Mathematische Modelle der Photonik
Dr. Jin Yan, WIAS Berlin:
Dichotomic randomness in simple and complex systems
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Many complex systems are a combination of deterministic and stochastic dynamics. Some systems can be understood by applying random perturbation theory to the underlying deterministic dynamics. However, generally the randomness may not necessarily be small and could consist of any type of stochasticity. Here, we consider a simplest case where only two types (i.e., dichotomic) of dynamics are generated randomly in time, and explore in (1) a simple piecewise-linear random system where either an expanding or contracting map is selected at each time iteration, and (2) a system of coupled rotors kicked with temporally correlated random sequences. In both examples, we illustrate analytically and numerically their rich dynamical behaviour.

Host
WIAS Berlin
Thursday, 29.02.2024, 10:00 (WIAS-405-406)
Software and Data Seminar
Dr. Jan Philipp Thiele, WIAS:
Advanced git: stashing, rebasing, bug hunting and the likes
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Host
WIAS Berlin
Wednesday, 28.02.2024, 14:00 (WIAS-ESH)
Forschungsseminar Mathematische Modelle der Photonik
Lasse Ermoneit, WIAS Berlin:
Optimal control of a quantum bus for scalable semiconductor quantum computing architectures
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Scaling up quantum processors to a large number of qubits to enable the implementation of error-correction algorithms is one of the major challenges on the path to realizing universal quantum computers. Spin qubits in gate-defined SiGe quantum dots provide excellent prospects for scalability, however the lithographic processing, signal routing and wiring of large qubit arrays at a small footprint poses a significant challenge [1]. One possible solution could be to separate the qubit register into small dense qubit arrays, which are interconnected by a quantum bus that allows for coherent transfer of quantum information by physically moving electrons between distant nodes along a channel [2]. Limitations in qubit shuttling arise from the interaction of the electron with material defects within the channel that can cause non-adiabatic transitions to excited states. As excited (orbital) states have a modified effective g-factor, this results in an accumulation of a random phase which finally diminishes the fidelity. In this contribution, we theoretically explore the capabilities for bypassing defect centers using optimally engineered control signals that allow for a quasi-adiabatic passage of the electron through the channel without reducing the velocity. Our approach is based on quantum optimal control theory and Schrödinger wave packet propagation using realistic potential landscapes.
References:
[1] Vandersypen et al., npj Quantum Inf. 3, 34 (2017)
[2] Langrock et al., PRX Quantum 4, 020305 (2023)
Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy - The Berlin Mathematics Research Center MATH+ (EXC-2046/1, project ID 390685689).

Further Informations
Forschungsseminar Mathematische Modelle der Photonik

Host
WIAS Berlin
Thursday, 22.02.2024, 10:00 (WIAS-405-406)
Software and Data Seminar
Marco Reidelbach; Silvia Polla:
MaRDMO: a tool for mathematical research data management
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Host
WIAS Berlin
Wednesday, 21.02.2024, 14:00 (WIAS-Library)
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Dr. Ioannis Papadopoulos, WIAS Berlin:
Computing multiple solutions of topology optimization problems
more ... Location
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411

Abstract
Topology optimization finds the optimal material distribution of a fluid or solid in a domain, subject to PDE and volume constraints. The models often result in a PDE, volume and inequality constrained, nonconvex, infinite-dimensional optimization problem that may support many local minima. In practice, heuristics are used to obtain the global minimum, but these can fail even in the simplest of cases. In this talk, we will introduce the deflated barrier method, a second-order algorithm that solves such problems, has local superlinear convergence, and can systematically discover many of these local minima. We will present examples which include finding 42 solutions of the topology optimization of a fluid satisfying the Navier-Stokes equations and more recent work involving the three-dimensional topology optimization of a fluid in Stokes flow. Underpinning the algorithm is the deflation mechanism. Deflation prevents a Newton-like solver from converging to a solution that has already been discovered. Deflation is computationally cheap, it does not affect the conditioning of the discretized systems, it may be coupled with a finite difference, finite volume or finite element discretization, and it is easy to implement.

Further Informations
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations

Host
WIAS Berlin
February 21, 2024 (WIAS-ESH)
Workshop/Konferenz: MATh.en.JEANS
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin
Tuesday, 20.02.2024, 15:30 (WIAS-ESH)
Seminar Interacting Random Systems
Utkir Rozikov, Uzbekistan Institute of Mathematics:
Gibbs measures of Potts model on trees
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
The talk is devoted to Gibbs measures of the q-state Potts model on Cayley trees. We present recent results (since 2014) about all translation-invariant splitting Gibbs measures. In particular, some conditions on the parameters of the q-state Potts model will be given for the (non-) extremality of these measures in the set of all Gibbs measures.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Tuesday, 20.02.2024, 14:00 (WIAS-ESH)
Seminar Interacting Random Systems
Jia-Jie Zhu, WIAS Berlin:
Kernelization, Approximation, and Entropy-Dissipation of Gradient Flows: from Wasserstein to Fisher-Rao
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Motivated by various machine learning applications, we present a principled investigation of gradient flow dissipation geometry, emphasizing the Fisher--Rao-type gradient flows and the connections with Wasserstein space. Using the dynamic Benamou--Brenier formulation, we reveal a few precise connections between those flow dissipation geometries and commonly used machine learning tools such as Stein flows, kernel discrepancies, and nonparametric regression. In addition, we present analysis results in terms of Łojasiewicz type functional inequalities, with an explicit threshold condition for a family of entropy dissipation along the Fisher--Rao flows. Finally, we establish rigorous evolutionary $Gamma$-convergence for the Fisher--Rao type gradient flows obtained via regression, justifying the approximation beyond static pointwise convergence. Joint work with Alexander Mielke.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Tuesday, 20.02.2024, 10:15 (WIAS-ESH)
Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Dr. Martin Schmidt, Universität Trier:
A primer on bilevel optimization under uncertainty
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
As it is the case for “usual”, i.e., single-level, optimization problems, bilevel optimization problems can and most likely should be considered under uncertainty as well. In single-level optimization, uncertainty is due to noisy or incomplete data that defines the problem at hand. For bilevel optimization, the sources of uncertainty are richer. Besides data uncertainty, the two-player nature of these problems leads to cases in which (the observation of) the decision of the other player might be unknown to some extend - a setting that we call decision uncertainty and that cannot appear in single-level optimization.
In this talk, we give a brief overview over the young field of bilevel optimization under uncertainty and present a specific example for the modeling of decision uncertainty. Finally, we highlight the newly established connections between robust and bilevel optimization that might lead to a stronger connection of the two fields.
This talk is based on joint work with Yasmine Beck, Marc Goerigk, Jannis Kurtz, Ivana Ljubic, and Johannes Thürauf.

Host
WIAS Berlin
Thursday, 15.02.2024, 10:00 (WIAS-ESH)
Software and Data Seminar
Fons van der Plas, Julia Lab, Massachusetts Institute of Technology:
Julia and Pluto.jl - is scientific computing accessible?
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Pluto's mission statement is to *make scientific computing more accessible and fun*! We all know that computers are fun, but what does it mean for computing to be *accessible*? More info: This talk highlights different areas of accessibility in scientific computing: - Taking skills into account: easy installation, simple API. - Taking learning backgrounds into account: documentation like "Julia for Matlab users" or "Pluto for Excel users". - Web accessibility: screen reader support, high-contrast mode. - Availability: free and open source, easy to find.

Host
WIAS Berlin
Wednesday, 14.02.2024, 14:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Ass. Prof. Dr. Kateryna Buryachenko, Humboldt-Universität zu Berlin / Vasyl' Stus Donetsk National University, Ukraine:
Regularity problems for anisotropic models
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 14.02.2024, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Christian Mönch, Johannes Gutenberg-Universität Mainz:
Inhomogenous long-range percolation: recent results
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
The Weight-Dependent Random Connection Model combines long-range percolation in Euclidean space with scale-free network models. The model and its variants have received considerable attention in the last few years. The talk aims to provide an overview of recent results, where special consideration will be given to the "weak decay regime". Here, connection probability tails are heavy enough to circumvent many geometrical difficulties that arise in short-range percolation models in low dimensions. I will summarise known sufficient conditions for existence and transience of an infinite cluster and discuss a local existence theorem which improves upon a result of Berger (2002) for homogeneous long-range percolation. The theorem is the main tool to establish continuity of the percolation function throughout the weak decay regime in dimension at least two. If time permits, I will discuss some open questions and future research goals. The talk is partly based on joint works with P. Gracar, L. Lüchtrath, M. Heydenreich and P. Mörters.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Wednesday, 14.02.2024, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. Dr. Martin Wahl, Universität Bielefeld:
Heat kernel PCA with applications to Laplacian eigenmaps
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Laplacian eigenmaps and diffusion maps are nonlinear dimensionality reduction methods that use the eigenvalues and eigenvectors of (un)normalized graph Laplacians. Both methods are applied when the data is sampled from a low-dimensional manifold, embedded in a high-dimensional Euclidean space. From a mathematical perspective, the main problem is to understand these empirical Laplacians as spectral approximations of the underlying Laplace-Beltrami operator. In this talk, we study Laplacian eigenmaps through the lens of kernel PCA, and consider the heat kernel as reproducing kernel feature map. This leads to novel points of view and allows to leverage results for empirical covariance operators in infinite dimensions.

Further Informations
Der Vortrag findet auch via Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Tuesday, 13.02.2024, 15:00 (WIAS-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Hans Kersting, Yahoo! Research:
Exploration and implicit bias due to an optimizer's stochasticity
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
The data sets used to train modern machine-learning models are often huge, e.g. millions of images. This makes it too expensive to compute the true gradient over all data sets. In each gradient descent (GD) step, a stochastic gradient is thus computed over a subset ("mini-batch?) of data. The resulting stochastic gradient descent (SGD) algorithm, and its variants, is the main workhorse of modern machine learning. Until recently, most machine-learning researchers would have preferred to use GD, if they could, and considered SGD only as a fast approximation to GD. But new research suggests that the stochasticity in SGD is part of the reason why SGD works so well. In this talk, we investigate multiple theories on the advantages of the noise in SGD, including better generalization in flatter minima (?implicit bias?) and faster escapes from difficult parts of the landscapes (such as saddle points and local minima). We highlight how correlating noise can help optimization and zoom in on the question which noise structure would be optimal for SGD.

Further Informations
Hybrid event. Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Tuesday, 13.02.2024, 13:30 (WIAS-406)
Seminar Materialmodellierung
Dr. Marcello Sega, University College London, GB:
Microscopic and mesoscopic simulations of fluid interfaces
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
I will present recent advancements in analyzing fluid interfaces from the microscopic to the mesoscopic scales. Beginning with the classical atomistic description of fluids in molecular dynamics simulations, I will discuss techniques for extracting surface information in the presence of thermal capillary waves. These modern numerical methods allow resolving the interface properties on a molecular layer basis, revealing a high degree of heterogeneity in their structure and transport coefficients. I will conclude by introducing a novel approach that bridges the microscopic and hydrodynamic scales, offering a more comprehensive understanding of droplet wetting dynamics at the mesoscopic level.

Further Informations
Seminar Materialmodellierung

Host
WIAS Berlin
Tuesday, 13.02.2024, 10:15 (WIAS-406)
Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Dr. Reinhold Schneider, Technische Universität Berlin:
Numerical solution of high-dimensional Hamilton Jacobi Bellmann (HJB) equations, mean field games and compositional tensor networks
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
The partial differential equations of Mean Field Games introduced by Lasry & Lions describe the solution of feedback optimal control problems as well as optimal transport problems. These equations play a fundamental role in optimal control, optimal transport, computational finance and machine learning. Therefore solving these kind of equations seems to be of outmost importance in future science and technology. However for solving these non-linear and high dimensional equations one has to deal with two major diffculties, namely 1) the curse of dimensions and secondly, a 2) possible lack of regularity. Here we focus only on the first issue. (The second problem can be relaxed by adding randomness, which is always present in practise.) We consider Potential Mean Field Games and are focusing on the (deterministic/stochastic) HJB. In order to compute semi-global solutions, we consider control affine dynamical systems and quadratic cost for the control as a prototype example. We follow an Lagrangian approach perspective, and a rcent approximation concept of compositional sparsity. In contrast to our earlier published semi-Lagrangian approaches, we describe a direct minimization of the total averaged cost over all initial values, first introduced by Kunisch & Walter (2021). Approximately, the true total cost is replaced by averaging over sampled initial values, where the sought approximate value function is parametrized in tensor form. Compositional sparsity has been inspired by Deep Neural Networks. The individual neural network layers are replaced by tree- based tensor networks (HT/TT) or sparse polynomials, which improves the stability for a numerical treatment of the optimization problem. Related literature: A machine learning framework for solving high-dimensional mean field game and mean field control problems, Ruthotto, Osher, Li, Nurbekyan, Fung - Proceedings of the National Academy of Sciences, 2020.

(joint work with M. Oster, RWTH Aachen)

Host
WIAS Berlin

Thursday, 08.02.2024, 10:00 (WIAS-405-406)
Software and Data Seminar
Dr. Jan Philipp Thiele, WIAS:
VSCode/VSCodium: using git and writing LaTeX
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Host
WIAS Berlin
Wednesday, 07.02.2024, 14:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Antonio Tribuzio, Universität Bonn:
Scaling laws for multi-well nucleation problems
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In this talk, we study scaling laws for nucleation problems which are motivated by models for shape-memory alloys. More precisely, we discuss optimal energy scaling of inclusions of a phase with several variants (martensite) inside a parent phase (austenite), for various model problems in two and three dimensions. The energy term is given by a singularly-perturbed multi-well elastic energy (without gauge invariances). We provide scaling results in the volume and the singular perturbation parameter for settings in which the surrounding parent phase is in the first-, the second- and the third-order lamination-convex hull of the wells of the "martensite phase". Furthermore, we provide a corresponding result for the setting of an infinite-order laminate which arises in the context of the Tartar square.

Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 07.02.2024, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Sabine Jansen, LMU München:
Infinite-dimensional Lie algebras, Lévy random fields and stochastic processes
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
Duality and intertwining help analyze Markov processes. Lie groups and orthogonal polynomials belong to analysis and geometry. What does one have to do with the other? I will discuss representations of the su(1,1) current algebra, with connections to: infinite-dimensional Meixner and Laguerre polynomials; negative binomial (Pascal) point processes and Gamma random measures; measure-valued branching processes and spatial birth-death processes. Based on joint works with Simone Floreani, Frank Redig and Stefan Wagner.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Wednesday, 07.02.2024, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
PhD Evgenii Chzhen, Université Paris-Saclay, Frankreich:
Small total-cost constraints in contextual bandits with knapsacks
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Der Vortrag findet auch via Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Tuesday, 06.02.2024, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Aleksei Kroshnin, WIAS Berlin:
Robust k-means in metric spaces
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
In this talk, we consider robust algorithms for the k-means clustering (quantization) problem where a quantizer is constructed based on an i.i.d. sample. While the well-known asymptotic result by Pollard shows that the existence of two moments is sufficient for strong consistency of an empirically optimal quantizer in a Euclidean space, non-asymptotic bounds are usually obtained under the assumption of bounded support. We discuss a robust k-means in metric spaces based on trimming (similar to the one proposed by Cuesta-Albertos et al. in 1997), and prove novel non-asymptotic bounds on the excess distortion depending on the optimal distortion rather then the second moment of the distribution. In particular, this bound decreases the gap to the lower bound obtained by Bartlett et al. (1998).

Further Informations
Hybrid event. Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Thursday, 01.02.2024, 11:30 (WIAS-ESH)
Seminar Interacting Random Systems
Jan Niklas Latz, Czech Academy of Sciencest & Charles University:
Monotone interacting particle systems: survival and the upper invariant law
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We consider monotone interacting particle systems for which the all-zero state is a trap. There are two important notions that characterize the "extinction" of such a system. One criterion for extinction is that the probability of the process never hitting the all-zero state, if started in a finite state, is zero for all such states. Another criterion is that the upper invariant law, the weak limit of the law of the process started in the greatest state, is the Dirac measure on the all-zero state. Both concepts are closely related via duality. In this talk I will explore their relation in detail.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Thursday, 01.02.2024, 10:00 (WIAS-405-406)
Software and Data Seminar
Dr. Jan Philipp Thiele, WIAS:
Introduction to version control with git
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Host
WIAS Berlin
Wednesday, 31.01.2024, 10:00 (WIAS-406)
Forschungsseminar Mathematische Statistik
PhD Gianluca Finocchio, Universität Wien, Österreich:
An extended latent factor framework for ill-posed linear regression
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
The classical latent factor model for linear regression is extended by assuming that, up to an unknown orthogonal transformation, the features consist of subsets that are relevant and irrelevant for the response. Furthermore, a joint low-dimensionality is imposed only on the relevant features vector and the response variable. This framework allows for a comprehensive study of the partial-least-squares (PLS) algorithm under random design. In particular, a novel perturbation bound for PLS solutions is proven and the high-probability L²-estimation rate for the PLS estimator is obtained. This novel framework also sheds light on the performance of other regularisation methods for ill-posed linear regression that exploit sparsity or unsupervised projection. The theoretical findings are confirmed by numerical studies on both real and simulated data.

Further Informations
Der Vortrag findet auch via Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
January 29 – 31, 2024 (WIAS-ESH)
Workshop/Konferenz: Dynamic spatial random systems
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin
Thursday, 25.01.2024, 15:00 (WIAS-ESH)
Forschungsseminar Mathematische Modelle der Photonik
Dr. Eddie Nijholt, Imperial College London, GB:
Emergent hypernetworks in weakly coupled oscillators
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Tba

Further Informations
Forschungsseminar Mathematische Modelle der Photonik

Host
WIAS Berlin
Thursday, 25.01.2024, 14:00 (WIAS-ESH)
Forschungsseminar Mathematische Modelle der Photonik
Prof. Tiago Pereira, University of São Paulo, Brasilien:
Chaotic behaviour in the Turing-Smale problem
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In the early fifties, Turing thought of the emergent oscillatory behavior due to diffusive interaction as a model for morphogenesis. In the mid-seventies, Smale proposed an example of diffusion-driven oscillations. Smale posed a problem of finding conditions under which diffusively coupled systems would oscillate. This problem was addressed in the context of the emergence of periodic solutions. Starting from a situation where each isolated node possesses a globally attracting equilibrium point, we give general conditions for an arbitrary network configuration for the existence of the diffusive coupling of a homogeneous strength which makes the network dynamics chaotic. This is a joint work with Eddie Nijholt, Fernando Queiros and Dmitry Turaev.

Further Informations
Forschungsseminar Mathematische Modelle der Photonik

Host
WIAS Berlin
Wednesday, 24.01.2024, 14:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Anastasija Pešić, Humboldt-Universität zu Berlin:
Variational models for pattern formation in biomembranes
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Biological membranes are thin structures that are composed of various components. The different components often form microdomains, called lipirafts, that are arranged in complex patterns. To explain this pattern formation, variational models based on Cahn--Hilliard type energies have been introduced that couple the local composition of the membrane to its local curvature, which renders the resulting functionals nonlocal. The main focus of this talk lies on the derivation of the Gamma-limit in a certain parameter regime where the limiting functional turns out to be of perimeter-type. As a main novelty, we will present a technique to include Neumann-boundary conditions in the construction of a recovery sequence. Additionally, in the remaining parameter regimes scaling behavior of the infimal energy will be discussed.

Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 24.01.2024, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Alessandra Faggionato, La Sapienza, Rome:
Transport in weighted Delaunay triangulations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
We consider the Delaunay triangulation (thought of as graph dual to the Voronoi tessellation) built on a simple point process in R^d, together with a random conductance field assigning a positive weight (conductance) to each non-oriented edge. We focus on several forms of transport, as random walks, resistor networks and symmetric simple exclusion processes defined on the above weighted Delaunay triangulation. By applying general results obtained in the last years, we derive their large scale limits. We then introduce generic (non-symmetric) exclusion processes whose definition is well posed under a suitable assumption of subcriticality for a percolation in a random environment. We give sufficient conditions assuring the above subcriticality.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Wednesday, 24.01.2024, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. Simon Wood, University of Edinburgh, GB:
On neighbourhood cross validation
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Cross validation comes in many varieties, but some of the more interesting flavours require multiple model fits with consequently high cost. This talk shows how the high cost can be side-stepped for a wide range of models estimated using a quadratically penalized smooth loss, with rather low approximation error. Once the computational cost has the same leading order as a single model fit, it becomes feasible to efficiently optimize the chosen cross-validation criterion with respect to multiple smoothing/precision parameters. Interesting applications include cross-validating smooth additive quantile regression models, and the use of leave-out-neighbourhood cross validation for dealing with nuisance short range autocorrelation. The link between cross validation and the jackknife can be exploited to obtain reasonably well calibrated uncertainty quantification in these cases.

Further Informations
Der Vortrag findet auch via Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Tuesday, 23.01.2024, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Luca Pelizzari, WIAS Berlin:
Rough PDEs for local stochastic volatility models
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
In this talk, we introduce a novel pricing methodology in general, possibly non-Markovian local stochastic volatility (LSV) models. We observe that by conditioning the LSV dynamics on the Brownian motion that drives the volatility, one obtains a time-inhomogeneous Markov process. Using tools from rough path theory, we describe how to precisely understand the conditional LSV dynamics and reveal their Markovian nature. The latter allows us to connect the conditional dynamics to so-called rough partial differential equations (RPDEs), through a Feynman-Kac type of formula. In terms of European pricing, conditional on realizations of one Brownian motion, we can compute conditional option prices by solving the corresponding linear RPDEs, and then average over all samples to find unconditional prices. Our approach depends only minimally on the specification of the volatility, making it applicable for a wide range of classical and rough LSV models, and it establishes a PDE pricing method for non-Markovian models. This talk is based on joint work with Peter Bank, Christian Bayer and Peter Friz.

Further Informations
Hybrid event. Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Thursday, 18.01.2024, 10:00 (WIAS-405-406)
Software and Data Seminar
Dr. Juergen Fuhrmann, WIAS:
Organizing research code projects in Julia
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Host
WIAS Berlin
Wednesday, 17.01.2024, 14:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Michael O'Donovan, WIAS Berlin:
Localization landscape theory: An overview and outlook
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 17.01.2024, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
PhD Matteo Giordano, Università degli Studi di Torino, Italien:
Likelihood methods for low frequency diffusion data
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
The talk will consider the problem of nonparametric inference in multi-dimensional diffusion models from low-frequency data. Implementation of likelihood-based procedures in such settings is a notoriously delicate task, due to the computational intractability of the likelihood. For the nonlinear inverse problem of inferring the diffusivity in a stochastic differential equation, we propose to exploit the underlying PDE characterisation of the transition densities, which allows the numerical evaluation of the likelihood via standard numerical methods for elliptic eigenvalue problems. A simple Metropolis-Hastings-type MCMC algorithm for Bayesian inference on the diffusivity is then constructed, based on Gaussian process priors. Furthermore, the PDE approach also yields a convenient characterisation of the gradient of the likelihood via perturbation techniques for parabolic PDEs, allowing the construction of gradient-based inference methods including MLE and Langevin-type MCMC. The performance of the algorithms is illustrated via the results of numerical experiments. Joint work with Sven Wang.

Further Informations
Der Vortrag findet auch via Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Tuesday, 16.01.2024, 15:00 (WIAS-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Benjamin Walker, University of Oxford, GB:
Log neural controlled differential equations: The lie brackets make a difference
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
Log neural controlled differential equations: The lie brackets make a difference The vector field of a controlled differential equation (CDE) describes the relationship between a control path and the evolution of a solution path. Neural CDEs (NCDEs) parameterise a CDE's vector field using a neural network, treat time series data as observations from a control path, and use the solution path as their hidden state. Given a partition of time, the Log-ODE method approximates the solution of a CDE by replacing it with an autonomous ODE on each interval. Building on the approach of neural rough differential equations (NRDEs), we introduce Log-NCDEs, which are the first application of the Log-ODE method to NCDEs. On a range of multivariate time series classification benchmarks, Log-NCDEs are shown to achieve an average test set accuracy higher than both NCDEs and NRDEs, and inline with current state-of-the-art deep learning methods.

Further Informations
Hybrid event. Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Friday, 12.01.2024, 13:00 (WIAS-Library)
E-Coffee-Lecture
Thomas Bender/Torsten Koehler/Jan Philipp Thiele, WIAS:
New WIAS Presentation Slides and Poster Styles - Remarks on design principles and technical implementation
more ... Location
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411

Abstract
In view of the upcoming evaluation we introduce a new design and its implementation for WIAS presentation slides and posters. To facilitate its use we will present both the underlying design principles and considerations as well as some aspects of the use of the styles templates for LaTeX, MS Powerpoint and Apple Keynote.

Host
WIAS Berlin
Wednesday, 10.01.2024, 14:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
PD Dr. Isabelle Schneider, Freie Universität Berlin:
Symmetry groupoids of dynamical systems
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Symmetries described by group transformations help immensely in our task to qualitatively characterize solutions of dynamical systems - providing that they exist. In this talk based on my habilitation thesis, we significantly enlarge the class of dynamical systems which can be studied by symmetry methods, moving our focus from groups to groupoids as the underlying algebraic structure describing symmetry. Building on the groupoid framework, we fundamentally generalize the notion of equivariance and equivariant bifurcation theory. We will also outline first applications in modelling and control of dynamical systems.

Further Informations
Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 10.01.2024, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Wolfgang König, WIAS Berlin:
A PhD project on dormancy in population dynamics in random environment (Part II)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Wednesday, 10.01.2024, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. Éric Moulines, Centre de Mathématiques Appliquées de l'Ecole Polytechnique (CMAP), Frankreich:
Score-based diffusion models and applications
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Deep generative models represent an advanced frontier in machine learning. These models are adept at fitting complex data sets, whether they consist of images, text or other forms of high-dimensional data. What makes them particularly noteworthy is their ability to provide independent samples from these complicated distributions at a cost that is both computationally efficient and resource efficient. However, the task of accurately sampling a target distribution presents significant challenges. These challenges often arise from the high dimensionality, multimodality or a combination of these factors. This complexity can compromise the effectiveness of traditional sampling methods and make the process either computationally prohibitive or less accurate. In my talk, I will address recent efforts in this area that aim to improve traditional inference and sampling algorithms. My major focus will be on score-based diffusion models. By utilizing the concept of score matching and time-reversal of stochastic differential equations, they offer a novel and powerful approach to generating high-quality samples. I will discuss how these models work, their underlying principles and how they are used to overcome the limitations of conventional methods. The talk will also cover practical applications, demonstrating their versatility and effectiveness in solving complex real-world problems.

Further Informations
Der Vortrag findet auch via Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Tuesday, 09.01.2024, 15:00 (WIAS-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Hannes Kern, TU Berlin:
Application of stochastic multiparameter sewing to regularity of local times associated to Gaussian sheets
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
In this talk, we shortly present the stochastic multiparameter sewing lemma, before focussing on the main topic: Its application to local times. We derive novel regularity estimates for local times of locally non-deterministic Gaussian sheets. These estimates are strong enough to show regularization by noise for SDEs in the plain. In this context, we make the observation that regularization effects profiting from the parameters of the underlying fields in an additive fashion usually appear due to boundary terms of the driving stochastic field.

Further Informations
Hybrid event. Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Wednesday, 20.12.2023, 14:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Georg Heinze, WIAS Berlin:
Graph-based nonlocal gradient flows and their local limits
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In this talk I will discuss systems of multiple nonlocally interacting species on a large class of graphs ranging from finite graphs to continuous graphs or graphons. The proposed analytical model is based on the theory of metric gradient flows and provides a unified upwind-based framework, including concave mobilities and non-1-homogeneous kinetic relations. Exploiting the systems gradient flow nature, we prove existence of weak solutions by establishing a rigorous link to a variational formulation in a quasi-metric setting. In addition, the behaviour of the arising dynamics is explored in numerical and analytical case studies, showcasing phenomena such as the formation of patterns, the aggregation of one species or the separation of different species. Finally, we will see for linear mobility and 1-homogeneous kinetic relation that solutions of nonlocal systems, defined on a suitable family of graphons, converge to solutions of a system of nonlocal interaction equations in Euclidean space.

Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 19.12.2023, 14:00 (WIAS-ESH)
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Dr. Joachim Rehberg, WIAS Berlin:
Maximal parabolic regularity for the treatment of real world problems
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
This is a series of three lectures on non-smooth problems, the first dedicated to elliptic ones and the third to parabolic ones. We start by explainig what means 'nonsmooth' and describe effects which cancel classical regularity results. Then we introduce a general geometric setting which allows in consequence to prove elliptic regularity results sufficient for attacking two- and three dimensional real world problems.
Having this at hand, elliptic operators on the scale of (negatively indexed) Sobolev spaces and Lp spaces are introduced and their regularity properties are investigated, among them L estimates, Hölder estimates and W 1,q estimates for the solution. After these preparations we pass to parabolic equations in the third and last lecture. Here the notion of 'maximal parabolic regularity' for an elliptic operator A is the central one - being now for some decades the ultimative instrument also for the investigation in particular of nonlinar problems. Since into this notion the domain of A enters explicitly, it becomes clear that an exact knowledge of dom(A), prepared in the first two lectures, is highly desirable. So, after having introduced maximal parabolic regularity and explained some of its properties, we show that second order divergence operators satisfy this property even if the domain is highly non-smooth, the coefficient function is only bounded, measurable and elliptic and the boundary conditions are mixed

Further Informations
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations

Host
WIAS Berlin
Tuesday, 19.12.2023, 10:15 (WIAS-406)
Seminar Nichtlineare Optimierung und Inverse Probleme
Mathias Oster, RWTH Aachen:
Going deep with dictionaries: ODE-based models
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Host
WIAS Berlin
Monday, 18.12.2023, 14:00 (WIAS-ESH)
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Dr. Clarice Poon, University of Warwick, UK:
Super-resolved Lasso
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Super-resolution of pointwise sources is of utmost importance in various areas of imaging sciences. Specific instances of this problem arise in single molecule fluorescence, spike sorting in neuroscience, astrophysical imaging, radar imaging, and nuclear resonance imaging. In all these applications, the Lasso method (also known as Basis Pursuit or l1-regularization) is the de facto baseline method for recovering sparse vectors from low-resolution measurements. This approach requires discretization of the domain, which leads to quantization artifacts and consequently, an overestimation of the number of sources. While grid-less methods, such as Prony-type methods or non-convex optimization over the source position, can mitigate this, the Lasso remains a strong baseline due to its versatility and simplicity. In this work, we introduce a simple extension of the Lasso, termed “super-resolved Lasso" (SR-Lasso). Inspired by the Continuous Basis Pursuit (C-BP) method, our approach introduces an extra parameter to account for the shift of the sources between grid locations. Our method is more comprehensive than C-BP, accommodating both arbitrary real-valued or complex-valued sources. Furthermore, it can be solved similarly to the Lasso as it boils down to solving a group-Lasso problem. A notable advantage of SR-Lasso is its theoretical properties, akin to grid-less methods. Given a separation condition on the sources and a restriction on the shift magnitude outside the grid, SR-Lasso precisely estimates the correct number of sources.

Further Informations
Hybrid event; Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations

Host
WIAS Berlin
Friday, 15.12.2023, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. Dr. Laura Sangalli, Politecnico di Milano, Italien:
Physics-informed spatial and functional data analysis
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Recent years have seen an explosive growth in the recording of increasingly complex and high-dimensional data, whose analysis calls for the definition of new methods, merging ideas and approaches from statistics and applied mathematics. My talk will focus on spatial and functional data observed over non-Euclidean domains, such as linear networks, two-dimensional manifolds and non-convex volumes. I will present an innovative class of methods, based on regularizing terms involving Partial Differential Equations (PDEs), defined over the complex domains being considered. These Physics-Informed statistical learning methods enable the inclusion of the available problem specific information, suitably encoded in the regularizing PDE. Illustrative applications from environmental and life sciences will be presented.

Further Informations
Der Vortrag findet auch via Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Thursday, 14.12.2023, 16:00 (WIAS-ESH)
Forschungsseminar Mathematische Modelle der Photonik
Robert Finn, Tyndall National Institute:
UV light emitters: from alloy microstructure to carrier transport
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin
Thursday, 14.12.2023, 14:30 (WIAS-ESH)
Seminar Numerische Mathematik
Christos Panagiotis Papanikas, WIAS Berlin / University of Cyprus:
From medical data to 3D modeling: simulation of cancer growth in mouse liver
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
The goal of this talk is to present in detail the different steps to construct a realistic 3D cancer growth model from medical data. In the first part, the type of available data will be discussed (MRI of mouse liver - courtesy of the MRE Group of the Charité), presenting how a tetrahedral mesh can be constructed using open-source software. In the second part, the definition of a mathematical model of cancer growth will be discussed, taking into account both biological and mechanical processes. The implementation and preliminary numerical results will also be presented. This work has been done in the context of my Erasmus+ stay at WIAS.

Further Informations
Numerics Seminar (FG3+LG5)

Host
WIAS Berlin
Wednesday, 13.12.2023, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Beatriz Salvador, Technical University of Lisbon, Portugal:
From duality to correlations: Application to the partial exclusion process SEP(alpha)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
In this talk, we introduce the concept of Stochastic Duality. From it, we will see an approach, based on duality, on how to bound the k-points centered correlation functions of a given interacting particle system (IPS) when it has the duality property and also a specific type of duality function. The problem of finding such bounds is an essential tool in order to derive the non-equilibrium fluctuations of a boundary-driven IPS. We will see an application of those results for the symmetric simple partial exclusion process with open boundary, i.e. SEP(alpha). Our aim is to obtain the decay (with respect to the size of the system) of its 2-points centered correlation function and generalize the result for the k-points centered correlation function, for kinmathbbN and kgeq 2. The case k=2 is joint work with Patrícia Gonçalves, Milton Jara, and Chiara Franceschini [1] and the general case is a work in progress with Patrícia Gonçalves. [1] Franceschini, C., Gonçalves, P., Jara, M., Salvador, B. (2023): Non-equilibrium fluctuations for SEP(alpha) with open boundary, submitted and online at https://arxiv.org/abs/2308.09144.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Wednesday, 13.12.2023, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Dr. Boris Buchmann, Australian National University, Australien:
Weak subordination of multivariate Levy processes
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Subordination is the operation which evaluates a Levy process at a subordinator, giving rise to a pathwise construction of a "time-changed" process. In probability semigroups, subordination was applied to create the variance gamma process, which is prominently used in financial modelling. However, subordination may not produce a levy process unless the subordinate has independent components or the subordinate has indistinguishable components. We introduce a new operation known as weak subordination that always produces a Levy process by assigning the distribution of the subordinate conditional on the value of the subordinator, and matches traditional subordination in law in the cases above. Weak subordination is applied to extend the class of variance-generalised gamma convolutions and to construct the weak variance-alpha-gamma process. The latter process exhibits a wider range of dependence than using traditional subordination. Joint work with Kevin W. LU - Australian National University (Australia) & Dilip B. Madan - University of Maryland (USA)

Further Informations
Hybrid Event. Der Vortrag findet auch via Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Tuesday, 12.12.2023, 15:00 (WIAS-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Prof. Leonid Berlyand, Pennsylvania State University, USA:
Asymptotic stability in a free boundary PDE model of active matter
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
We discuss applications of random matrix theory (RMT) to the training of deep neural networks (DNNs). Our numerical results show that if the drastic reduction of DNN parameters is guided by the Marchenko-Pastur spectral approach, then the accuracy of the pruned DNN and CNN with much fewer parameters does not decrease. For fully connected DNNs the accuracy actually increases. Moreover, the deviation from the mean is smaller for the non-pruned DNNs. Furthermore, we show how this RMT can be used to remove 10-12% of parameters from state-of-the-art DNNs such as Resnet and VIT without reducing and even increasing accuracy. Finally, we provide a theoretical understanding of these results by proving the Pruning Theorem that establishes a rigorous relation between the accuracy of the pruned and non-pruned DNNs. This is joint work with E. Sandier, Y. Shmalo and L. Zhang.

Further Informations
Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Tuesday, 12.12.2023, 13:30 (WIAS-ESH)
Seminar Numerische Mathematik
Jan Philipp Thiele, WIAS Berlin:
Error-controlled space-time finite elements, algorithms and implementations for nonstationary problems
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Recently, many advances have been done in the field of space-time finite element discretizations for nonstationary partial differential equations. The temporal dimension leads to additional costs in solving the equations, so adaptive finite element methods can lead to sufficiently accurate solutions at a better efficiency compared to uniform refinement. Additionally, the solution to the equation itself is often not of direct interest, but instead some derived quantity has to be calculated accurately. For this, the dual-weighted residual (DWR) method offers a practical way to calculate estimators for the temporal and spatial error parts with respect to the unknown exact value of that quantity. This talk introduces the extension of the partition-of-unity localization (PU) for non-stationary problems, which provides error indicators for use in marking strategies. For the tensor-product space-time approach we developed the library ideal.II which extends the library deal.II to simplify the implementation of non-stationary problems. We brieftly discuss some of the design decisions and technical details of this library. Both the library and the PU-DWR method are validated by several numerical studies with linear and nonlinear PDEs.

Further Informations
Numerics Seminar (FG3+LG5)

Host
WIAS Berlin
Thursday, 07.12.2023, 10:00 (WIAS-405-406)
Seminar Interacting Random Systems
Giovanni Conforti, École Polytechnique, Paris:
Invariant integrated convexity profiles for Hamilton-Jacobi-Bellman equations and applications
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
It has been known for a long time that Hamilton-Jacobi-Bellman (HJB) equations preserve convexity, namely if the terminal condition is convex, the solution stays convex at all times. Equivalently, log-concavity is preserved along the heat equation, namely if one starts with a log-concavity density, then the solution stays log-concave at all times. Both these facts are a direct consequence of Prékopa-Leindler inequality. In this talk, I will argue that carrying out a second-order analysis of coupling by reflection on the characteristics of the HJB equation prompts the existence of weaker notions of convexity that propagate backward along HJB equations. More precisely, by introducing the notion of integrated convexity profile, we are able to construct families of functions that fail to be convex, but are still invariant under the action of the HJB equation. In the second part of the talk I will illustrate some applications of these invariance results to functional inequalities, in particular to the construction of Lipschitz maps, and to the exponential convergence of learning algorithms for entropic optimal transport.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Wednesday, 06.12.2023, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Dennis Nieman, Vrije Universiteit Amsterdam, Niederlande:
Frequentist guarantees for variational Gaussian process regression (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We discuss the variational Bayesian approach with inducing variables introduced by Titsias (2009). This is a sparse approximation for the Bayesian posterior distribution in the nonparametric Gaussian process regression model. The procedure is analyzed from a frequentist perspective: we study contraction rates and validity of the uncertainty quantification. Specifically, it is shown how the frequentist properties of the variational posterior depend on the chosen prior distribution and the dimension of the approximation. Most of the theory is developed under the assumption that the smoothness of the true, data-generating parameter is known, but we also discuss a smoothness-adaptive variational procedure.

Further Informations
Der Vortrag findet auch via Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Westfälische Wilhelms-Universität Münster
Tuesday, 05.12.2023, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Pavel Dvurechensky, WIAS Berlin:
Decentralized local stochastic extra-gradient for variational inequalities (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
We consider distributed stochastic variational inequalities (VIs) on unbounded domains with the problem data that is heterogeneous (non-IID) and distributed across many devices. We make a very general assumption on the computational network that, in particular, covers the settings of fully decentralized calculations with time-varying networks and centralized topologies commonly used in Federated Learning. Moreover, multiple local updates on the workers can be made for reducing the communication frequency between the workers. We extend the stochastic extragradient method to this very general setting and theoretically analyze its convergence rate in the strongly-monotone, monotone, and non-monotone (when a Minty solution exists) settings. The provided rates explicitly exhibit the dependence on network characteristics (e.g., mixing time), iteration counter, data heterogeneity, variance, number of devices, and other standard parameters. As a special case, our method and analysis apply to distributed stochastic saddle-point problems (SPP), e.g., to the training of Deep Generative Adversarial Networks (GANs) for which decentralized training has been reported to be extremely challenging. In experiments for the decentralized training of GANs we demonstrate the effectiveness of our proposed approach. Joint work with A. Beznosikov, A. Koloskova, V. Samokhin, S. Stich, A. Gasnikov.

Further Informations
Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Thursday, 30.11.2023, 16:00 (WIAS-406)
Forschungsseminar Mathematische Modelle der Photonik
Thomas Tenzler, Ferdinand-Braun-Institut:
Simulation of the generation of entangled photons through spontaneous parametric down conversion in Bragg-reflection-waveguide lasers based on AlGaA
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Host
WIAS Berlin
Ferdinand-Braun-Institut, Leibniz-Institut für Höchstfrequenztechnik
Wednesday, 29.11.2023, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Robert I. A. Patterson, WIAS Berlin:
Gradient flows and the exclusion process
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
I will recall the concept of a generalised gradient flow and how this can be applied to the time marginals of a Markov process which admits detailed balance. I will then summarise how this is applied to a speed changed exclusion process that is in detailed balance with respect to a Gibbs measure and talk about spectral gaps and convergence to local equilibrium. This is then a tool in analysing the hydrodynamic limit of the exclusion process, which is itself a second gradient flow. This will be an informal talk with imprecise definitions and I will mention some open problems relevant to my project with Julian Kern.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Wednesday, 29.11.2023, 10:00 (WIAS-HVP-3.13)
Forschungsseminar Mathematische Statistik
Prof. Dr. Martin Spindler, Universität Hamburg:
High-dimensional L2-boosting: Rate of convergence (hybrid talk)
more ... Location
Weierstraß-Institut, Hausvogteiplatz 11A, 10117 Berlin, 3. Etage, Raum: 3.13

Further Informations
Der Vortrag findet auch via Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Tuesday, 28.11.2023, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Christophe Roux, Zuse-Institut Berlin:
Bounding geometric penalties in first-order Riemannian optimization (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
Riemannian optimization is the study of optimizing functions defined over Riemannian manifolds. This paradigm is used in cases that naturally present Riemannian constraints, which allows for exploiting the geometric structure of our problem, and for transforming it into an unconstrained one by working in the manifold. Convergence rates of Riemannian optimization algorithms often rely on geometric quantities depending on the sectional curvature and the distance between iterates and an optimizer. Numerous previous works bound the latter only by assumption, leading to an incomplete analysis and unquantified rates. In this talk, I will discuss how to remove this limitation for multiple algorithms and as a result quantify their rates of convergence. In particular, I will present results on deterministic first-order minimization algorithms such as Gradient Descent and the (Inexact) Proximal Point Algorithm as well as min-max algorithms such as the Extra Gradient Method.

Further Informations
Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
November 28 – 30, 2023 (WIAS-ESH)
Workshop/Konferenz: MaRDI Annual Workshop 2023
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin
Thursday, 23.11.2023, 14:00 (WIAS-405-406)
Seminar Numerische Mathematik
Grégoire Pourtier, Technische Universität Berlin:
A Julia-based universal solver for system of one-dimensional nonlinear PDEs
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
In this talk, we introduce a new Julia library designed for solving universal systems of one-dimensional elliptic and parabolic partial differential equations. This library is based on the API from the MATLAB solver pdepe, and the spatial discretization follows the finite element method described in the paper of Skeel and Berzins [1]. The library enables the use of time integration methods from the DifferentialEquations.jl package [2]. Its primary focus is on achieving high performance by minimizing allocations within the core code loops and using Julia?s optimization tools to ensure code stability. We present various tools employed in the library?s implementation, including the concept of Automatic Differentiation and its application to sparse operator. We also provide explanations and recommendations for specific choices made during development. Additionally, we include convergence tests for both the spatial and time discretization as well as a test case on the modeling of Lithium Ion Batteries [3] and benchmark results comparing the Julia library with the MATLAB solver pdepe. Finally, we introduce an extension designed to address 1D+1D problems for multi-scale modeling.

Further Informations
Numerics Seminar (FG3+LG5)

Host
WIAS Berlin
Wednesday, 22.11.2023, 10:00 (WIAS-406)
Forschungsseminar Mathematische Statistik
Prof. Dr. Marc Hoffmann, Université Paris-Dauphine:
On estimating multidimensional diffusions from discrete data (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Further Informations
Der Vortrag findet auch via Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Tuesday, 21.11.2023, 17:00 (Online Event)
Seminar Materialmodellierung
Jan Grebik, University of California Los Angeles:
Large deviation principles for graphon sampling
more ... Location
Online Event

Abstract
Let G(n,p) be the random graph on [n] vertices, where each edge is added independently with probability p . Using the theory of dense graph limits, so-called graphons, Chatterjee and Varadhan established a large deviation principle (LDP) for this model, which they used to investigate properties of a typical graph under the assumption that a rare event has occurred. In this talk I will discuss LDP for general graphon sampling with particular emphasis on block graphons. Here the setup is as follows; a graphon W:[0,1]2?[0,1] is a symmetric Lebesgue measurable function and G(n,W) is the random graph on [n] vertices, where we first sample x1,?,xn?[0,1] independently according to the Lebesgue measure and then add the edge between vertices k,??[n] independently with probability W(xk,x?) . We describe a LDP for G(n,W) in the case when W is a so-called step graphon, and hint on why finding LDP for sampling from a general graphon seems to be a difficult problem. Time permitting, we compare our work with a recent result by Borgs, Chayes, Gaudio, Petti and Sen on LDP for block models. This is a joint work with O.Pikhurko.

Further Informations
Seminar Materialmodellierung

Host
WIAS Berlin
Monday, 20.11.2023, 14:00 (WIAS-406)
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Dr. Joachim Rehberg, WIAS Berlin:
Regularity for non-smooth elliptic problems II
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
This is a series of three lectures on non-smooth problems, the first dedicated to elliptic ones and the third to parabolic ones. We start by explainig what means 'nonsmooth' and describe effects which cancel classical regularity results. Then we introduce a general geometric setting which allows in consequence to prove elliptic regularity results sufficient for attacking two- and three dimensional real world problems.
Having this at hand, elliptic operators on the scale of (negatively indexed) Sobolev spaces and Lp spaces are introduced and their regularity properties are investigated, among them L estimates, Hölder estimates and W 1,q estimates for the solution. After these preparations we pass to parabolic equations in the third and last lecture. Here the notion of 'maximal parabolic regularity' for an elliptic operator A is the central one - being now for some decades the ultimative instrument also for the investigation in particular of nonlinar problems. Since into this notion the domain of A enters explicitly, it becomes clear that an exact knowledge of dom(A), prepared in the first two lectures, is highly desirable. So, after having introduced maximal parabolic regularity and explained some of its properties, we show that second order divergence operators satisfy this property even if the domain is highly non-smooth, the coefficient function is only bounded, measurable and elliptic and the boundary conditions are mixed

Further Informations
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations

Host
WIAS Berlin
November 20 – 22, 2023 (WIAS-ESH)
Workshop/Konferenz: Dynamics in Coupled Network Systems
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin
Thursday, 16.11.2023, 14:00 (WIAS-ESH)
Seminar Numerische Mathematik
Dr. Francesco Romor, WIAS Berlin:
Efficiently solving parametric PDEs on solution manifolds parametrized by neural networks
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
A slow decaying Kolmogorov n-width of the solution manifold of a parametric partial differential equation precludes the realization of efficient linear projection-based reduced-order models. This is due to the high dimensionality of the reduced space needed to approximate with sufficient accuracy the solution manifold. To solve this problem, neural networks, in the form of different architectures, have been employed to build accurate nonlinear regressions of the solution manifolds. However, the majority of the implementations are non-intrusive black-box surrogate models, and only a part of them perform dimension reduction from the number of degrees of freedom of the discretized parametric models to a latent dimension. We present a new intrusive and explicable methodology for reduced-order modelling that employs neural networks for solution manifold approximation but that does not discard the physical and numerical models underneath in the predictive/online stage. We will focus on autoencoders used to compress further the dimensionality of linear approximants of solution manifolds, achieving in the end a nonlinear dimension reduction. After having obtained an accurate nonlinear approximant, we seek for the solutions on the latent manifold with the residual-based nonlinear least-squares Petrov-Galerkin method, opportunely hyper-reduced in order to be independent from the number of degrees of freedom.

Further Informations
Numerics Seminar (FG3+LG5)

Host
WIAS Berlin
Wednesday, 15.11.2023, 14:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
PD Dr. Lutz Recke, Humboldt-Universität zu Berlin:
A common approach to singular perturbation and homogenization
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 15.11.2023, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Elena Magnanini, WIAS Berlin:
Gelation and hydrodynamic limits in cluster coagulation processes
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
A coagulation process describes the behavior of a particle system where families of particles (or clusters) merge as time passes. Specifically, we consider the so-called cluster coagulation model introduced by Norris in 2000. One of the main differences w.r.t. the classical Marcus-Lushnikov process is that this model is able to incorporate various features (not only the mass) in the evolution of clusters, such as their locations. The coagulation mechanism is regulated by a kernel, that is a positive symmetric function of the two clusters. Depending on the choice of this function, clusters whose masses are on a significantly larger scale than most others in the system, could emerge in finite time. This kind of phase transition is known as gelation. We provide sufficient criteria for gelation extending (and sometimes improving) results related to the classical Marcus--Lushnikov process. In some special cases the cluster coagulation process can be coupled with an inhomogeneous random graph; in this context we are able to identify an upper bound for the gelation time in terms of the critical parameter that determines the appearance of a giant component in the inhomogeneous random graph. We complete our analysis by showing that the trajectories associated with the process concentrate on solutions of an infinite system of measure valued differential equations that generalize the Flory equation. Joint work with L. Andreis and T. Iyer.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Tuesday, 14.11.2023, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Leonard Schmitz, Universität Greifswald:
Two-parameter sums signatures and corresponding quasisymmetric functions (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
Quasisymmetric functions have recently been used in time series analysis as polynomial features that are invariant under, so-called, dynamic time warping. We extend this notion to data indexed by two parameters and thus provide warping invariants for images. We show that two-parameter quasisymmetric functions are complete in a certain sense, and provide a two-parameter quasi-shuffle identity. A compatible coproduct is based on diagonal concatenation of the input data, leading to a (weak) form of Chen's identity.

Further Informations
Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Monday, 13.11.2023, 13:30 (WIAS-ESH)
Berlin Oberseminar: Optimization, Control and Inverse Problems
Dr. Helene Frankowska, Sorbonne Université, France:
Differential inclusions and optimal control on Wasserstein spaces
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Optimal Control on Wasserstein spaces addresses control of systems with large number of agents. Recently many models arising in social sciences use these metric spaces of Borel probability measures. The aim of this talk is to demonstrate that for Lipschitz kind dynamics, some corner stone results of classical control theory known in the Euclidean framework have their analogues in Wasserstein spaces. In this talk I will first discuss an extension of the theory of differential inclusions to the setting of general Wasserstein spaces. Indeed, it is well known that for optimal control of ODEs, the differential inclisions theory provides useful tools to investigate existence of optimal controls, necessary optimality conditions and Hamilton-Jacobi-Bellman equations. Same happens for Wasserstein spaces. In particular, I will present necessary and sufficient conditions for the existence of solutions to state-constrained continuity inclusions from [2] building on a suitable notion of contingent cones in Wasserstein spaces leading to viability and invariance theorems. They were already applied in [5], [6] to investigate stability of controlled continuity equations and uniqueness of solutions to HJB equations and will be recalled by the end of the talk. (Please find the contents of the footnotes under the seminar link given above)

Further Informations
Berlin Oberseminar: Optimization, Control and Inverse Problems

Host
WIAS Berlin
Thursday, 09.11.2023, 15:30 (WIAS-405-406)
Seminar Materialmodellierung
Prof. Dr. Rupert Klein, Freie Universität Berlin:
Thoughts on machine learning
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
Techniques of machine learning (ML) find a rapidly increasing range of applications touching upon social, economic, and technological aspects of everyday life. They are also being used with great enthusiasm to fill in gaps in our scientific knowledge by data-based modelling approaches. I have followed these developments for a while with interest, concern, and mounting disappointment. When these technologies are employed to take over decisive functionality in safety-critical applications, we would like to exactly know how to guarantee their compliance with pre-defined guardrails and limitations. Moreover, when they are utilized as building blocks in scientific research, it would violate scientific standards -- in my opinion -- if these building blocks were used without a throrough understanding of their functionality, including inaccuracies, uncertainties, and other pitfalls. In this context, I will juxtapose (a subset of) deep neural network methods with the family of entropy-optimal Sparse Probabilistic Approximation (sSPA) techniques developed recently by Illia Horenko and colleagues.

Further Informations
Seminar Materialmodellierung

Host
WIAS Berlin
Wednesday, 08.11.2023, 14:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Tomáš Roubíček, Czech Academy of Sciences, Tschechische Republik:
Some gradient theories in linear visco-elastodynamics towards dispersion and attenuation of waves in relation to large-strain models
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
First, the standard viscoelastic rheologies of the Kelvin--Voigt, Maxwell's, and Jeffreys' types are analyzed in linear one-dimensional situations as far as the propagation of waves and their dispersion and attenuation. Then various spatial-gradient extensions are examined. These gradient extensions are then presented in the large-strain variants where they are sometimes used rather for purely analytical reasons either in the Lagrangian or the Eulerian formulations. The relation of such gradient viscoelastic models with propagation of waves is thus illuminated. A reference: Preprint arXiv no.2309.05089, Sept. 2023.

Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 08.11.2023, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Dr. Sven Wang, Humboldt-Universität zu Berlin:
Statistical convergence rates for transport- and ODE-based generative models (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Measure transport provides a powerful toolbox for estimation and generative modelling of complicated probability distributions. The common principle is to learn a transport map which couples a tractable (e.g. uniform or normal) reference distribution to some complicated target distribution, e.g. by maximizing a likelihood objective. In this talk, we discuss recent advances in statistical convergence guarantees for such methods. While a general theory is developed, we will primarily treat (1) triangular maps which are the building blocks for “autoregressive normalizing flows" and (2) ODE-based maps, defined through an ODE flow. The latter encompasses NeuralODEs, a popular method for generative modeling. Our results imply that transport methods achieve minimax-optimal convergence rates for non-parametric density estimation over Hölder classes on the unit cube. Joint work with Youssef Marzouk (MIT, United States), Robert Ren (MIT, United States) and Jakob Zech (U Heidelberg, Germany).

Further Informations
Der Vortrag findet auch via Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Tuesday, 07.11.2023, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Prof. Dr. Peter K. Friz, TU & WIAS Berlin:
On (local) rough stochastic volatility and weak rates (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
Stocks, futures, commodities and exchange rates share very similar statistical features The self-organising mechanism through which all markets appear to settle close to such a critical point remains a mystery. From a pure engineering point of view, rough volatility has gotten us “a step closer to the perfect volatility model" (Bouchaud 2020), and this talk is devoted to a better mathematical understanding thereof. In part 1 we consider simple rough stochastic volatility specifications itentify the optimal weak rate of convergence, out of reach of classical PDE based methods, which stabilises in the “very" rough regime when $H$ is close to zero, popular in econophysics. Part 2 is devoted to general stochastic volatility (including but not restricted to a rough volatility scale) in presence of an additional leverage functions. Such local stochastic volatility models come with popular data-driven particle methods, yet well-posedness remains largely open. As remedy we propose to consider instead an Euler discretisation, trivially well-posed, and show that it achieves an eps-perfect calibration for eps Euler steps in time. This is joint work with W. Salkeld (Brown University, Part 1) and T. Wagenhofer (TU Berlin, Part 1 & 2).

Further Informations
Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Friday, 03.11.2023, 10:00 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Ass. Prof. Hannes Meinlschmidt, Friedrich-Alexander Universität Erlangen-Nürnberg:
Renormalized solutions for optimal control of the drift in Fokker--Planck equations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 01.11.2023, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Fredi Tröltzsch, Technische Universität Berlin:
Optimal control of partial differential equations - selected results and recent trends
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In its first part, the talk introduces to some main results of the optimal control theory for partial differential equations. In particular, first-order necessary and second-order sufficient optimality conditions for semilinear elliptic and parabolic equations are discussed. The second part addresses applications of these principles of optimal control theory to the control of some reaction-diffusion equations. Moreover, recent trends in the theory are briefly outlined.

Further Informations
Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 01.11.2023, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Wolfgang König, WIAS Berlin:
Two PhD projects: dense Erdős--Rényi graphs, and dormancy in population dynamics in random environment
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
We present the background and the goals in two current PhD projects. (1) We ask about the typical behaviour of a dense Erdős--Rényi graph, when conditioned on having a very large number of triangles and/or bonds, or under an exponential transformation that favours these numbers. The goal is to extend this into a spatial setting. (2) The parabolic Anderson model (PAM) with random potential describes the expected population size of a branching particle system in a random potential (here time-dependent) . Dormancy is the ability of the particles to fall asleep (hence not taking part of the reproduction anymore, but having a higher protection from dangers coming from the environment) and to wake up later. This is a random strategy of the particle cloud to protect against random extinction. The effects coming from inserting such a strategy into the PAM is to be analysed.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Wednesday, 01.11.2023, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. Dr. Victor Panaretos, École Polytechnique Fédérale de Lausanne, Schweiz:
Optimal transport for covariance operators (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Covariance operators are fundamental in functional data analysis, providing the canonical means to analyse functional variation via the celebrated Karhunen-Loève expansion. These operators may themselves be subject to variation, for instance in contexts where multiple functional populations are to be compared. Statistical techniques to analyse such variation are intimately linked with the choice of metric on covariance operators, and the intrinsic infinite-dimensionality and of these operators. I will describe how the geometry and tools of optimal transportation can be leveraged to construct natural and effective statistical summaries and inference tools for covariance operators, taking full advantage of the nature of their ambient space. Based on joint work with Valentina Masarotto (Leiden), Leonardo Santoro (EPFL), and Yoav Zemel (EPFL).

Further Informations
Der Vortrag findet auch via Zoom statt: https://zoom.us/j/159082384

Host
WIAS Berlin
Tuesday, 31.10.2023, 10:15 (WIAS-406)
Seminar Nichtlineare Optimierung und Inverse Probleme
Dr. Dan Tiba, Romanian Academy, Bucharest:
Topology optimization and boundary observation for clamped plates
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Host
WIAS Berlin
Wednesday, 25.10.2023, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. Dr. Denis Belomestny, Universität Duisburg-Essen:
Provable benefits of policy learning from human preferences (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
A crucial task in reinforcement learning (RL) is a reward construction. It is common in practice that no obvious choice of reward function exists. Thus, a popular approach is to introduce human feedback during training and leverage such feedback to learn a reward function. Among all policy learning methods that use human feedback, preference-based methods have demonstrated substantial success in recent empirical applications such as InstructGPT. In this work, we develop a theory that provably shows the benefits of preference-based methods in tabular and linear MDPs. The main idea of our method is to use KL-regularization with respect to the learned policy to ensure more stable learning.

Further Informations
Der Vortrag findet auch via Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Tuesday, 24.10.2023, 10:00 (WIAS-ESH)
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Dr. Amal Alphonse, WIAS Berlin:
Analysis of a variational contact problem arising in thermoelasticity
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We study a model of a thermoforming process involving a membrane and a mould as implicit obstacle problems. Mathematically, the model consists of parabolic and elliptic PDEs coupled to a (quasi-)variational inequality. We study the related stationary (elliptic) model. We look at the existence of weak solutions, and by exploring the fine properties of the contact set under non-degenerate data, we give sufficient conditions for the existence of regular solutions. Under certain contraction conditions, we also show a uniqueness result. This is based on a joint paper with Jose-Francisco Rodrigues (Lisbon, Portugal) and Carlos N. Rautenberg (Virginia, USA).

Further Informations
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations

Host
WIAS Berlin
Thursday, 19.10.2023, 16:00 (WIAS-ESH)
Forschungsseminar Mathematische Modelle der Photonik
Dr. Mindaugas Radziunas, WIAS Berlin:
Calculation of optical modes in large emission area photonic crystal surface-emitting lasers
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We discuss numerical challenges in constructing and resolving spectral problems for photonic crystal surface-emitting lasers with large (up to several mm^2) emission areas. We show that finite difference schemes with moderate and large domain discretization steps provide sufficient accuracy of several major (lowest-threshold) modes of constructed systems

Further Informations
Forschungsseminar Mathematische Modelle der Photonik

Host
WIAS Berlin
Wednesday, 18.10.2023, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Simone Floreani, Universität Bonn:
Universal properties of non-equilibrium steady states of boundary-driven symmetric systems
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
In this talk, using stochastic duality, I will prove universal properties of stationary measures of boundary-driven symmetric (partial) exclusion process and inclusion process. More precisely, I will show a universal structure of the n point non-equilibrium correlations and a probabilistic representation of the stationary measure. Finally, In the case of the simple symmetric open exclusion process, I will provide a probabilistic alternative to the matrix ansatz to obtain explicit formulas.
Based on joint works with Adrián González Casanova, Frank Redig and Federico Sau.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Thursday, 12.10.2023, 14:00 (WIAS-ESH)
Seminar Numerische Mathematik
Dr. Hang Si, Cadence Austin Office, USA:
Perspectives of anisotropic Delaunay mesh adaptation
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Anisotropic meshes are essential to improve the efficiency and accuracy of numerical solutions. Generating anisotropic meshes remains a challenging problem in both theory and applications. In this talk, we address this topic from an application point of view. In particular, we show applications in surface meshing and numerical solutions. We will review the mathematical principles of anisotropic mesh adaptation and explore the connection with quasi-conformal mapping theory. We then discuss practical metric-based Delaunay algorithms to generate anisotropic meshes. We finish with some remarks on software implementation.

Further Informations
Numerics Seminar

Host
WIAS Berlin
Thursday, 12.10.2023, 10:15 (WIAS-406)
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Dr. Mazen Ali, Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM:
Quantum Computing for Differential Equations and Surrogate Modeling
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
Quantum computing has transitioned from theoretical promise to practical reality, with multiple devices now accessible to the public. This technological evolution has catalyzed a multidisciplinary race to achieve the first 'quantum advantage,' drawing experts from fields as diverse as physics, computer science, finance, mathematics, and chemistry. However, despite the immense potential, the practical utility of current quantum computing implementations remains modest. Much of the research is concentrated on similar, easily-attainable goals, often accompanied by overstated claims and unwarranted optimism. Consequently, pivotal questions about the true nature of 'quantum advantage,' the roadmap to achieving it, and its fundamental relevance remain unanswered. Our focus is on harnessing the capabilities of quantum computing for material simulations at the macroscopic scale. In this presentation, I will offer an overview of the current state of quantum computing, discuss methodologies for solving differential equations directly on quantum platforms, and explore the use of quantum machine learning to create surrogate models for complex systems.

Further Informations
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations

Host
WIAS Berlin
October 12, 2023 (HU Berlin HVP)
Workshop/Konferenz: First NFDI-Berlin-Brandenburg meeting
more ... Location
Humboldt-Universität zu Berlin, Hausvogteiplatz 5-7, R. 0007

Host
WIAS Berlin
Wednesday, 11.10.2023, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Bas Lodewijks, Universität Augsburg:
Long-range first-passage percolation on the complete graph
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
We consider first-passage percolation on the complete graph Kn, where vertices have a spatial position on the d-dimensional torus. For α ≥ 0, each edge e in the graph is assigned an independent transmission time Te, which is the product of a rate-one exponential random variable and the spatial length of the edge, raised to the power alpha. When α =0 we obtain the non-spatial case of first-passage percolation on the complete graph.
We study the behaviour of the random metric induced by the transmission times in the case that α < d. In particular, we investigate the typical distance, flooding time, and diameter of the graph, and obtain results akin to the well-established results for the α=0 case. If time permits, we shall also look into on-going work on competing long-range first-passage percolation, where two infections with possibly different transmission times occupy the vertices of the graph over time. Here, we investigate the possibility of coexistence, among other things.

Mostly joint work with Remco van der Hofstad, and partially with Neeladri Maitra.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin

Wednesday, 04.10.2023, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Reinhard Scholz, Leibniz-Institut für Polymerforschung Dresden:
Simulation amphiphiler Polymernetzwerke
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Polymere bestehen aus langen Ketten chemisch identischer oder ähnlicher Monomere. In biologischen Systemen kommen solche Systeme u.a. als Proteine und Energiespeicher vor, sowie als Träger der Erbinformation. Für die Wechselwirkung mit Lösungsmittelmolekülen spielen spezielle biologische Funktionen keine wesentliche Rolle, was eine vergröberte statistische Beschreibung ermöglicht, in der nur noch zwischen den Monomeren des Polymers und den Lösungsmittelmolekülen unterschieden wird. Amphiphile Polymere bestehen aus mindestens zwei Arten von Teilketten, die unterschiedlich mit einem Lösungsmittel wechselwirken können. Die Synthese solcher Systeme erfolgt in einem guten Ko-Lösungsmittel für alle Bestandteile. Anschließend kann ein anderes Lösungsmittel gewählt werden, das nur eine Komponente gut löst, während eine andere Komponente nicht gelöst wird, so dass Strukturen auf einer Nanometerskala entstehen. Im Rahmen der DFG-geförderten Forschergruppe 2811 Ädaptive Polymergele mit kontrollierter Netzwerkstruktur" werden gezielt amphiphile Netzwerke aus Sternpolymeren aufgebaut. Die mit experimentellen Methoden gefundenen Eigenschaften werden mit theoretischen Modellen und Simulationen interpretiert. In diesem Vortrag wird insbesondere auf das Quellverhalten solcher Netzwerke und auf die Strukturbildung im selektiven Lösungsmittel eingegangen.

Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 04.10.2023, 14:00 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Dorothee Knees, Universität Kassel:
Regularity results for a static relaxed micromorphic model
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
The relaxed micromorphic model is a generalized continuum model allowing to describe for instance size effects of microstructured solids. The state of the solid subject to external loads is characterized by the displacement field u : R3 ⊃ Ω → R3 and the microdistortion tensor P : Ω → R 3x3. The corresponding system of partial differential equations consists of the system of linear elasticity that is coupled with a system of Maxwell type for the distortion tensor P. We will discuss the regularity of weak solutions under different assumptions on the smoothness of the domain. The main ingredients for the proofs are the Helmholtz decomposition and refined difference quotient arguments based on generalized inner variations in combination with a Piola-type transformation. This is ongoing joint work with Patrizio Neff (Duisburg-Essen) and Sebastian Owczarek (Warsaw).

Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 04.10.2023, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Subhro Ghosh, National University of Singapore:
Rigidity phenomena in strongly correlated random point fields and the emergence of forbidden regions
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
The aim of this talk is to give an introduction to recent results concerning rigidity properties of random point fields, focussing in particular on the associated phenomenon of forbidden regions. Rigidity phenomena pertain to the emergence of singularities in strongly correlated point processes (e.g. those related to random matrices, Coulomb gases, zeros of random polynomials and random sections of line bundles), wherein local conservation laws have been shown to hold true. This includes, e.g., local conservation laws for mass or centre of mass, conditioned on the environment (ie the configuration of points outside a given domain). Such rigidity phenomena have been shown to be closely related to the emergence of novel `forbidden regions' in the spatial distribution of points conditioned on important classes of rare events. In particular, spatial holes (i.e. vacant domains) of macroscopic size (at the scale of the droplet) in strongly rigid point fields have been shown to enforce the emergence of complementary holes (of comparable scale) in other parts of the space.


Based in part on the following joint works.
[1] Rigidity and Tolerance in point processes: Gaussian zeroes and Ginibre eigenvalues, with Y. Peres, Duke Math. J., 166(10), 1789-1858
[2] Gaussian complex zeros on the hole event: the emergence of a forbidden region, with A. Nishry, Comm. Pure Appl. Math. 72(1), 3-62
[3] Approximate Gibbsian structure in strongly correlated point fields and generalized Gaussian zero ensembles, with U. Gangopadhyay, K.A. Tan, Comm. Pure Appl. Math., to appear
[4] Forbidden regions for random zeros on Riemann surfaces, with T.C. Dinh, H. Wu, near completion

Host
WIAS Berlin

Wednesday, 04.10.2023, 10:00 (WIAS-ESH)
Seminar Interacting Random Systems
Tiffany Y.Y. Lo, Uppsala University, Sweden:
The expected degree distribution in duplication divergence models
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We study the degree distribution of a randomly chosen vertex in a duplication-divergence graph, paying particular attention to what happens when a non-trivial proportion of the vertices have large degrees, establishing a central limit theorem for the logarithm of the degree distribution. Our approach, as in Jordan (2018) and Hermann and Pfaffelhuber (2016), relies heavily on the analysis of related birth-catastrophe processes. This is joint work with A. D. Barbour.

Host
WIAS Berlin
Wednesday, 04.10.2023, 10:00 (WIAS-406)
Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Dr. Pedro Pérez-Aros, Universidad de O'Higgins, Chile:
Coderivative-based semi-Newton method in nonsmooth difference programming
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
In this presentation, we explore a new category of challenging nonsmooth optimization problems. These problems involve the difference between generally nonconvex functions as their objective. We introduce an innovative Newton-type algorithm designed for solving such problems. This algorithm leverages advanced tools from variational analysis and is based on the concept of the coderivative generated second-order subdifferential (generalized Hessian). We discuss the algorithm's well-posedness properties, establishing its viability under broad conditions. Additionally, we analyze its convergence rates, incorporating assumptions such as the Kurdyka-Lojasiewicz condition. The talk ends with some numerical experiments which ilustrate the performance of our development.

Host
WIAS Berlin
Wednesday, 27.09.2023, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Michiel Renger, TU München:
Collisions in the exclusion process
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
The simple symmetric exclusion process (SSEP) and a system of independent random walkers both converge to the same diffusion equation. To understand the difference, we count the number of times a SSEP particle would have jumped if the particles were independent, but did not jump because the target site was occupied. This number can also be interpreted as the number of times two SSEP particles collide. We show its hydrodynamic limit using Markov duality. In fact, we are interested in a whole zoo of related microscopic variables, and if time allows I will briefly talk about their large deviations. Ongoing work with Mario Ayala (TUM).

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Monday, 25.09.2023, 10:00 (WIAS-ESH)
Seminar Materialmodellierung
Leonardo Araujo, Technische Universität München:
Beyond the Born--Oppenheimer approximation by Surface Hopping Trajectories methods
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In molecular dynamics, the Born--Oppenheimer approximation is a fundamental concept, assuming the decoupling of electronic and nuclear motions due to the significant mass difference between them. This implies that, from the perspective of the nuclei, the electrons effectively reside in an eigenstate. While this approximation is widely employed in quantum chemistry to expedite molecular wavefunction calculations, it encounters limitations, especially in scenarios involving light atoms and high-energy systems. In the first part of this presentation, we confront this limitation by going beyond the Born--Oppenheimer approximation and adding multiple electronic eigenstates into the approximation. We will discuss the theory of this approach and present the resulting equations of motion for the nuclei. Moving on to the second part, we explore computationally efficient methods for simulating such dynamics by considering a class of quantum-classical methods: the Surface Hopping Trajectories. These methods entail an ensemble of trajectories, sampled from the initial nuclear configuration, performing classical dynamics on the eigensurface of an electronic eigenstate. They further allow each trajectory to undergo transitions to different eigenstates guided by hopping probabilities. We present two famous versions of Surface Hopping: the Fewest-Switches Surface Hopping (FSSH) and the Single Switch Surface Hopping (SSSH), also recognised as Landau--Zener Surface Hopping. To culminate, we illustrate the use of these methods through a practical example using WavePacket, a Matlab software package for quantum-mechanical and quantum-classical simulations.

Further Informations
Seminar Materialmodellierung

Host
WIAS Berlin
Tuesday, 19.09.2023, 15:15 (WIAS-ESH)
Oberseminar Nonlinear Dynamics
Dr. Sebastian Eydam, RIKEN - Center for Brain Science, Japan:
Metabolic feedback and its potential role in epilepsy
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Epilepsy, a widespread neurological disorder, affects a substantial portion of the global population, with approximately 30% of cases proving resistant to conventional pharmacological interventions. This resistance arises from the heterogeneous nature of epilepsy's underlying etiologies, rendering it a complex spectrum of disorders rather than a singular disease entity. While expert neurologists can tailor treatment approaches to individual patients, a significant number of cases remain refractory to available therapies. An alternative avenue for mitigating epilepsy lies in revisiting historical practices such as fasting, which has been reported to reduce seizures back in antiquity. In the early 20th century, this concept evolved into the ketogenic diet (KD), a structured dietary regimen renowned for its efficacy in reducing epileptic seizures [1]. Nonetheless, with the emergence of modern anti-epileptic drugs (AEDs), dietary interventions received limited research attention for several decades, only experiencing resurgence in recent years. In this presentation, we introduce a model featuring quadratic integrate-and-fire neurons coupled to a global energy reservoir. The inclusion of this energy reservoir simulates the transition from a standard diet to a ketogenic one. Our proposed mechanism for seizure control hinges on the presence of ATP-dependent potassium channels [2], whose activity, or lack thereof in the presence of ATP, results in neuronal hyperpolarization. Our findings support the viability of this mechanism for regulating epileptic activity in our model, demonstrating that adherence to a KD can shift neuronal dynamics back to a regime of normal activity. We substantiate this relationship by investigating bifurcations within a corresponding mean-field model [3] and presenting simulations that explore three distinct methods of transitioning between normal and seizure-like activity: ATP concentration shocks, parametric perturbations in ATP production rates, and external current stimulation.
[1] Lutas, Andrew & Yellen, Gary. The ketogenic diet: metabolic influences on brain excitability and epilepsy. Trends in Neurosciences , Vol. 36, No. 1, 2013.
[2] Joo, Pangyu et al. Network Model With Reduced Metabolic Rate Predicts Spatial Synchrony of Neuronal Activity. Frontiers in Computational Neuroscience , Vol. 15, (2021).
[3] Montbrió, Ernest; Pazó, Diego; Roxin, Alex . Macroscopic Description for Networks of Spiking Neurons, Physical Review X , Vol. 5, No. 2 , American Physical Society (APS), (2015).

Host
WIAS Berlin
September 18 – 22, 2023 (WIAS-ESH)
Workshop/Konferenz: ESGI 175 - the Berlin Study Group with Industry
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin
Thursday, 14.09.2023, 15:00 (WIAS-HVP-3.04)
Forschungsseminar Mathematische Modelle der Photonik
Lutz Mertenskötter, WIAS Berlin:
Estimation of frequency noise characteristics and data-driven modeling of narrow-linewidth semiconductor lasers
more ... Location
Weierstraß-Institut, Hausvogteiplatz 11A, 10117 Berlin, 3. Etage, Raum: 3.04

Further Informations
Forschungsseminar Mathematische Modelle der Photonik

Host
WIAS Berlin
Thursday, 14.09.2023, 14:00 (WIAS-HVP-3.04)
Forschungsseminar Mathematische Modelle der Photonik
Dr. Eduard Kuhn, WIAS Berlin:
Simulation of the mode dynamics in broad-ridge (Al,In)GaN laser diodes
more ... Location
Weierstraß-Institut, Hausvogteiplatz 11A, 10117 Berlin, 3. Etage, Raum: 3.04

Further Informations
Forschungsseminar Mathematische Modelle der Photonik

Host
WIAS Berlin
September 13 – 15, 2023 (WIAS-ESH)
Workshop/Konferenz: Energetic Methods for Multi-Component Reactive Mixtures: Modelling, Stability, and Asymptotic Analysis
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
The central theme of this workshop are mechanical models describing the transport of mass, momentum, and energy in multi-component mixtures, including diffusion, convection, and heat transfer. A consistent account of reactions is a further concern. EMRM 2023 focuses in particular on energetic and entropic tools for strongly coupled systems of hyperbolic--parabolic type, whose analysis is still underdeveloped and has received insufficient attention relative to their tremendous significance in real-world applications. Many complex physical processes not only involve mass transfer induced by random diffusion, but also reaction processes and directed transport including non-local drifts induced, for instance, by the interaction of electrically charged particles. The relative influence of these different processes will depend on the specific application. Developing a framework that asymptotically relates the different models is nowadays an active field of research in multi-component flow modelling. This workshop focuses on the analysis of multi-component mixtures using diffusion models and hydrodynamic models, on the analysis of complex evolutionary systems of hyperbolic--parabolic type, including multi-phase problems, as well as on the connections between these approaches by means of asymptotic analysis.

Host
WIAS Berlin
Technische Universität Wien
Tuesday, 12.09.2023, 10:15 (WIAS-ESH)
Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Dr. L'ubomír Baňas, Universität Bielefeld:
Robust adaptivity for the stochastic Cahn--Hilliard equation
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin
September 6, 2023 (HUB Luisenstrasse Festsaal)
Workshop/Konferenz: Colloquium on the Occasion of Alexander Mielke's 65th Birthday
more ... Location
Humboldt Universität zu Berlin, Luisenstrasse 56, 10117 Berlin, Festsaal

Abstract
Rupert Klein (FU Berlin): Mathematical modelling in geophysical fluid dynamics
Three examples from geophysical fluid dynamics will showcase mathematical modelling as the ärt of judicious simplification": The computational prediction of two seasonal to decadal phenomona, the "quasi-biennial oscillation" (QBO) and the "El Niño Southern Oscillation" (ENSO) became possible only after theoreticians had captured their essential causal structures in convincing reduced mathematical models. With our own research, we aim to similarly untangle the mechanisms behind the "rapid intensification" (RI) of tropical storms during their transition to hurricane strength.

Felix Otto (MPI Leipzig): Singular stochastic partial differential equations: More geometry and less combinatorics
Singular stochastic PDE are those stochastic PDE in which the noise is so rough that the nonlinearity requires a renormalization. The guiding principle of renormalization is to preserve as many symmetries of the solution manifold as possible. We follow the approach of mathematical physics, and of Hairer's regularity structures, which however we re-interpret as providing an informal parameterization of the infinite-dimensional nonlinear solution manifold. We systematically follow this more geometric/analytic than combinatorial point-of-view: Instead of appealing to an expansion indexed by trees, we consider all partial derivatives w.r.t. the "constitutive" function defining the nonlinearity. Instead of a Gaussian calculus guided by Feynman diagrams arising from pairing nodes of two trees, we consider derivatives w.r.t. the noise, i.e. Malliavin derivatives. We interpret the Malliavin derivative of the parameterization as an approximate tangent vector to the solution manifold, which yields a sparse representation in terms of the parameterization itself, and paves the way for its stochastic estimate. Ultimately, this gives a characterization of the solution manifold that is oblivious to the divergent counter terms. This is work with L. Broux, P. Linares, M. Tempelmayr, and P. Tsatsoulis, based on work with J. Sauer, S. Smith, and H. Weber.

Riccarda Rossi (U Brescia): Variational approaches to rate-independent and gradient systems
The mathematical analysis of rate-independent systems has sparked intensive research over the last two decades, both because they are ubiquitous in mechanics, and due to their intrinsic nonsmoothness, which poses several challenges. The work by Alexander Mielke has set a cornerstone in the field, starting with the weak solvability notion of Energetic solution. The Energetic concept has become paradigmatic for rate-independent evolution: one of its fingerprints is its variational character, which paves the way for the usage of the wide toolbox of Calculus of Variations in the analysis of specific systems. And, again, the interplay between rate-independent systems and the variational theory for gradient flows has inspired yet another concept, that of Balanced Viscosity solutions. A twitch upon the thread leads to Alexander's work on discrete systems, to EDP convergence... and to several intriguing open perspectives.

Host
Humboldt-Universität zu Berlin
WIAS Berlin
August 30 – September 1, 2023 (WIAS-ESH)
Workshop/Konferenz: Biophysics-based modeling and data assimilation in medical imaging 2023
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin
Charité - Universitätsmedizin Berlin
Tuesday, 29.08.2023, 14:00 (WIAS-ESH)
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Dr. Robert John Baraldi, Sandia National Laboratories, USA:
A proximal trust--region method for nonsmooth optimization with inexact function and gradient evaluations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We develop a novel trust-region method to minimize the sum of a smooth nonconvex function and a nonsmooth convex function. This class of problems that is ubiquitous in data science, learning, optimal control, and inverse problems. Our method is unique in that it permits and systematically controls the use of inexact objective function and derivative evaluations inherent in large-scale system solves and compression techniques, e.g. randomized sketching. When using a quadratic Taylor model for the trust-region subproblem, our algorithm is an inexact, matrix-free proximal Newton-type method that permits indefinite Hessians. We prove global convergence of our method in Hilbert space and elaborate on potential nonsmooth subproblem solvers based on ideas taken from their smooth counter-parts. Under additional assumptions, we can also prove superlinear, or even quadratic convergence to local minima. We demonstrate its efficacy on examples from data science and PDE-constrained optimization.

Further Informations
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations

Host
WIAS Berlin
Tuesday, 15.08.2023, 15:00 (WIAS-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Egor Gladin, Humboldt-Universität zu Berlin:
Accuracy certificates for convex minimization with inexact oracle (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
A notion of certificates for convex minimization problems allows to verify the accuracy of approximate solutions and provides a theoretically valid stopping criterion. When the dual optimization problem is solved, certificates produce a simple way to recover primal solution. In the talk, the notion of certificates is generalized to take into account the error in a first-order oracle. A recipe for computation of certificates for a large class of cutting plane methods is presented. As a by-product, we show that considered methods that were originally designed to be equipped with an exact oracle can also be efficiently used with a noisy oracle.

Further Informations
Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Thursday, 03.08.2023, 16:00 (WIAS-ESH)
Forschungsseminar Mathematische Modelle der Photonik
Prof. Dmitry Turaev, Imperial College London, GB:
Chaos in reversible homoclinic tangles
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
TBA

Host
WIAS Berlin
July 31 – August 2, 2023 (Harnack-Haus)
Workshop/Konferenz: Phase transitions in random point systems
more ... Location
Harnack-Haus -- Tagungsstätte der Max-Planck-Gesellschaft

Host
WIAS Berlin
DFG Schwerpunktprogramm 2265
Wednesday, 26.07.2023, 13:30 (WIAS-ESH)
Seminar Numerische Mathematik
Prof. Stefan Ringe, Korea University, Korea (Republik):
First-principles multi-scale modeling of electrochemical CO2 reduction
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Electrochemical CO2 reduction is a viable pathway towards reducing greenhouse gas emissions and establishing a sustainable energy landscape. Bringing this reaction to industrial competitiveness is thus of significant interest and subject of current research. Recent studies have shown that the reaction is very complicated and multi-scale of nature, involving the coupling of reaction kinetics, electric double layer and mass transport. Modeling this from the computational side offers valuable insights about the importance of cell design parameters, such as the electrolyte species, geometric dimensions and components of the electrolyzer, or solvent type. In this presentation, I present the steps from first-principles density functional theory calculations all the way up to multi-scale models which can help to understand experimentally observed trends and give suggestions about optimal parameters.

Further Informations
Numerics Seminar

Host
WIAS Berlin
Monday, 24.07.2023, 14:30 (WIAS-ESH)
Seminar Weierstrass Group Data-Driven Optimization and Control
PhD Anna Korba, École Nationale de la Statistique et de l'Administration Économique (ENSAE), Frankreich:
Sampling with mollified interaction energy descent (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Sampling from a target measure whose density is only known up to a normalization constant is a fundamental problem in computational statistics and machine learning. In this paper, we present a new optimization-based method for sampling called mollified interaction energy descent (MIED). MIED minimizes a new class of energies on probability measures called mollified interaction energies (MIEs). These energies rely on mollifier functions -- smooth approximations of the Dirac delta originated from PDE theory. We show that as the mollifier approaches the Dirac delta, the MIE converges to the chi-square divergence with respect to the target measure and the gradient flow of the MIE agrees with that of the chi-square divergence. Optimizing this energy with proper discretization yields a practical first-order particle-based algorithm for sampling in both unconstrained and constrained domains. We show experimentally that for unconstrained sampling problems our algorithm performs on par with existing particle-based algorithms like SVGD, while for constrained sampling problems our method readily incorporates constrained optimization techniques to handle more flexible constraints with strong performance compared to alternatives.

Further Informations
Der Vortrag findet auch via Zoom statt: https://us02web.zoom.us/j/8994552597

Host
WIAS Berlin
Thursday, 20.07.2023, 14:00 (WIAS-405-406)
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Olaf Klein, WIAS Berlin:
Uncertainty quantification for models involving hysteresis operators
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
Parameters within models involving hysteresis operators that are supposed to describe with real world objects like, e.g. magneto mechanical devices, have to be identified from measurements. Hence, they are subject to corresponding errors. The methods of Uncertainty Quantification (UQ) are applied to investigate the influence of these errors. As an example, results of forward UQ for a play operator with uncertain yield limit will be presented. Afterwards, the model for a magneto mechanical devices involving a generalized Prandtl-Ishlinskiĭ operator considered in Sec. 5 in Davino-Krejčí--Visone-2013, Fully coupled modeling of magneto-mechanical hysteresis through `thermodynamic' compatibility. Smart Mater. Struct. https://doi.org/10.1088/0964-1726/22/9/095009 will be considered. Starting from data used to generated a First-Order-Reversal-Curves (FORC)-diagram inverse UQ is performed by formulating appropriate Bayesian Inverse Problems (BIPs) and applying Bayes' Theorem. The density of the resulting posterior density is represented by samples resulting from MCMC-computations using UQLab, the “The Framework for Uncertainty Quantification”, see https://www.uqlab.com/. Afterwards, forward UQ is performed and the results are compared to measurements. These are results of a joined work with Carmine Stefano Clemente and Daniele Davino of the Università degli Studi del Sannio, Benevento, Italy and Ciro Visone of Università di Napoli Federico II, Napoli, Italy, see also: K.-Davino-Visone-2020, On forward and inverse uncertainty quantification for models involving hysteresis operators, Math. Model. Nat. Phenom 15, https://doi.org/10.1051/mmnp/2020009 and Clemente-Davino-K.-Visone-2023, Forward and Inverse Uncertainty Quantification for a model for a magneto mechanical device involving a hysteresis operator, WIAS Preprint 3009

Further Informations
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations

Host
WIAS Berlin
Thursday, 20.07.2023, 14:00 (WIAS-ESH)
Seminar Numerische Mathematik
David Brust, Deutsches Zentrum für Luft- und Raumfahrt (German Aerospace Center) DLR:
Modelling study of a photo-thermal catalytic reactor for rWGS reaction under concentrated Irradiation
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Utilization of CO2 via hydrogenation with H2 from carbon-free sources in the rWGS reaction offers a fossil-free pathway to the production of synthesis gas, which represents an important and versatile feedstock for the chemical industry. In this talk a photo driven catalytic reactor for the rWGS reaction operating under concentrated solar irradiation is investigated in a multi-physics modelling study. The numerical model covers chemical reactions relevant for rWGS conditions and considers coupled heat and multi-component mass transfer in the catalyst layer and porous support. For thermal evaluation of the porous modelling domain, the local thermal equilibrium (LTE) method is used, describing both the fluid phase and the solid structure by a single temperature field. Different relations for the effective thermal conductivity of the porous structure are compared. Radiation transport onto the irradiated surfaces is accounted for in a simplified manner. Multi-component mass transfer in the porous structure is described with the Dusty-gas Model. The transport equations for thermal energy and species mass together with boundary conditions are discretized in three space dimensions and solved with the finite-volume method via the open-source package VoronoiFVM.jl. The multi-physics model enables the analysis of energy losses and thus supports the optimization of reactor design and operation conditions.

Further Informations
Numerics Seminar

Host
WIAS Berlin
Wednesday, 19.07.2023, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Katharina Hopf, WIAS Berlin:
Structure, dynamics, and approximation of cross-diffusive mixtures with incomplete diffusion (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In population dynamics, cross-diffusion refers to the phenomenon where the density gradient of one species induces a drift in a different species. Mathematically speaking, cross-diffusion equations are quasilinear second-order systems of partial differential equations often featuring an additional structure related to their physical origin. Much of the existing theory on cross-diffusions is confined to Petrovskii parabolic systems. In this talk, we focus on a cross-diffusion system arising in population biology whose diffusion matrix is rank deficient, thus giving rise to an incomplete diffusion process. We exhibit a symmetric hyperbolic-parabolic structure of the PDE system and hence the short-time well-posedness of the Cauchy problem in spaces of smooth functions. By means of an extended framework of measure-valued solutions, we further discuss the long-time behaviour for large data as well as (numerical) approximation properties. This talk is based on joint works with Pierre-Etienne Druet and Ansgar Jüngel.

Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 19.07.2023, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. Dr. Giada Adelfio, Università degli Studi di Palermo, Italien:
Spatio-temporal point processes: Local second-order statistics for estimation and diagnostics (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In previous papers, we defined an approach to assesses the goodness-of-fit of spatio-temporal models, weighteing by the inverse of the conditional intensity function. The method accounts for the local weighted second-order statistics, providing a quite general approach for individual diagnostics. Starting from these results, we developed an estimation based on the local second-order characteristics of the weighted process, providing also local estimates. The method does not rely on any particular model assumption on the data, and thus it can be applied for whatever is the generator model of the (even complex) process. In addition, we want to account for the primary role of second-order statistics for improving inference of complex intensity functions, when likelihood could be intractable, and complex interactions may be not negligible for a proper description.

Further Informations
Der Vortrag findet auch via Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Tuesday, 18.07.2023, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
PhD Daniel J. Mankowitz, Google Deepmind, GB:
AlphaDev: Faster sorting algorithms discovered using deep reinforcement learning (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
Fundamental algorithms such as sorting or hashing are used trillions of times on any given day. As demand for computation grows, it has become critical for these algorithms to be as performant as possible. Whereas remarkable progress has been achieved in the past, making further improvements on the efficiency of these routines has proved challenging for both human scientists and computational approaches. Here we show how artificial intelligence can go beyond the current state of the art by discovering hitherto unknown routines. To realize this, we formulated the task of finding a better sorting routine as a single-player game. We then trained a new deep reinforcement learning agent, AlphaDev, to play this game. AlphaDev discovered small sorting algorithms from scratch that outperformed previously known human benchmarks. These algorithms have been integrated into the LLVM standard C++ sort library3. This change to this part of the sort library represents the replacement of a component with an algorithm that has been automatically discovered using reinforcement learning. We also present results in extra domains, showcasing the generality of the approach.

Further Informations
Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Tuesday, 18.07.2023, 14:30 (WIAS-ESH)
Seminar Numerische Mathematik
Dr. Roman Pascal Schaerer, Zürcher Hochschule für Angewandte Wissenschaften (ZHAW), CH:
A non-isothermal cell performance model for organic flow batteries
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Flow batteries are an emerging technology for large-scale stationary energy storage. Specifically, organic flow batteries (OFBs) have been proposed as a promising and more sustainable alternative to metal-based batteries. The large chemical space available for organic electro-active redox couples allows to optimize the chemical properties to the specific requirements of the battery system. Furthermore, local synthesis of organic electrolytes offers the advantage of greater sustainability and reduced supply chain risks. Electrochemical flow cells represent one of the core building blocks of flow battery stacks, where the conversion between electrical and chemical energy is performed. To analyse and improve the energy efficiency of flow cells, we developed a continuum-scale model for the performance prediction of a single flow cell. The model solves for the spatially resolved stationary solution of the coupled balance equations of mass, charge, momentum and energy densities over the cell domain, which includes the current collectors, porous electrodes and the ion-exchange membrane. The effective macroscopic transport properties of the porous electrodes are modelled using an up-scaling methodology based on the volume averaging method. This approach facilitates an investigation of the impact of the pore-scale geometry and transport characteristics on the macroscopic transport properties, such as the effective diffusivity and reaction rate. The model has been implemented in the Julia programming language and is published as open source software. The discretization of the balance equations is performed with the FV method implemented by the VoronoiFVM.jl package. First validation studies with a laboratory test cell using a fully organic electrolyte have shown promising results. The model will be used to explore the energy efficiency potential of a single flow cell with respect to the cell geometry and operating condition, such as flow rate and electrolyte concentrations.

Host
WIAS Berlin
Tuesday, 18.07.2023, 13:30 (WIAS-ESH)
Seminar Numerische Mathematik
Dr. Benoît Gaudeul, Université Paris-Saclay, Frankreich:
Building thermodynamically consistent models using variationnal modelling
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In this talk we sketch a modelling framework in which the diffusive fluxes stems from both the free energy and the dissipation of free energy in the second principle of thermodynamics. We use this framework to obtain various models from the literature and show how they can then be naturally extended to coupled physics. Finally we discuss briefly the inclusion of convective effects and equilibrium manifolds.

Further Informations
Numerics Seminar

Host
WIAS Berlin
Tuesday, 18.07.2023, 10:15 (WIAS-406)
Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Dr. Helmut Harbrecht, Universität Basel, Schweiz:
Low-rank tensor approximation of continuous functions
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Host
WIAS Berlin
July 17 – 21, 2023 (Harnack-Haus)
Workshop/Konferenz: SPP2265 Summer School: Probability and geometry on configuration spaces
more ... Location
Harnack-Haus -- Tagungsstätte der Max-Planck-Gesellschaft

Host
WIAS Berlin
DFG Schwerpunktprogramm 2265
Wednesday, 12.07.2023, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. David Padilla-Garza, Technische Universität Dresden:
Mathematical challenges and developments in the nonlinear bending theory for plates (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
The nonlinear bending theory for plates describes the mechanics of a thin inextensible and incompressible film. It features a highly non-convex isometry constraint and a quadratic cost on second-order terms. This talk will be about modern developments in deriving an extension of the nonlinear bending theory for new materials, in a mathematically general and rigorous way using Gamma-convergence. I will begin by deriving a nonlinear bending theory for prestrained thin films, using convex-integration solutions to the Monge--Ampere equation. I will also discuss nonlinear bending theories for microheterogeneous thin plates and liquid crystal elastomer bilayers.

Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 12.07.2023, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Andreas Klippel, TU Darmstadt:
Comparison of the random loop model to percolation and infinite loops in the random link model
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
Peter Mühlbacher showed for a graph of bounded vertex degree that the inverse temperature of the random loop model can be compared to a percolation parameter by stochastic domination. This leads to a bound where infinitely large loops do not occur. We use a different approach to improve this bound and obtain an explicit value. Only if the inverse temperature is chosen larger than the explicit value infinitely long loops can occur. Therefore, we introduce the so-called model of total orders which is a discretized model of the random loop model. Furthermore, we demonstrate how this domination argument could be applied to compare the random link model to percolation which is an ongoing project with Benjamin Lees. This is a joint work with Benjamin Lees and Mino Nicola Kraft.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Wednesday, 12.07.2023, 10:15 (WIAS-406)
Seminar Nichtlineare Optimierung und Inverse Probleme
Dr. Patrick Gelß, Zuse-Institut Berlin:
Fredholm integral equations for the training of shallow neural networks
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Host
WIAS Berlin
Wednesday, 12.07.2023, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. Dr. Mathias Vetter, Christian-Albrechts-Universität zu Kiel:
On goodness-of-fit testing for point processes (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Typical models for point processes like Hawkes processes or inhomogeneous Poisson processes are often of a parametric form where the intensity function or an additional self-exciting component is known up to an unspecified parameter. A lot of research since the seminal paper by Ogata (1978) has been devoted to the estimation of these unknown parameters but even in these rather standard models a consistent goodness-of-fit test has been missing. This talk aims to fill this gap. We will show how to formally set up a bootstrap procedure to allow for goodness-of-fit testing and we will discuss how to prove consistency of the test in the (already quite involved) case of an inhomogenous Poisson processes.

Further Informations
Der Vortrag findet auch via Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Tuesday, 11.07.2023, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Prof. Dr. Fanny Yang, ETH Zürich, Schweiz:
Surprising failures of standard practices in ML when the sample size is small (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
In this talk, we discuss two failure cases of common practices that are typically believed to improve on vanilla methods: (i) adversarial training can lead to worse robust accuracy than standard training (ii) active learning can lead to a worse classifier than a model trained using uniform samples. In particular, we can prove both mathematically and empirically, that such failures can happen in the small-sample regime. We discuss high-level explanations derived from the theory, that shed light on the causes of these phenomena in practice.

Further Informations
Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Tuesday, 11.07.2023, 13:30 (WIAS-ESH)
Seminar Numerische Mathematik
Derk Frerichs-Mihov, WIAS Berlin:
Using deep learning techniques to improve the discrete solution of convection-dominated convection-diffusion equations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Convection-diffusion equations are a basic model to describe the distribution of a scalar quantity in fluids. In the convection-dominated regime, the solution usually possesses so-called layers, which are small regions where the solution has a steep gradient. Unfortunately, it is well known in the literature that it is challenging for many classical methods to approximate the solution in these layers. The solution is often polluted by unphysical values, so-called spurious oscillations. In this talk, a deep learning-based slope limiter is presented, that automatically detects regions where the solution has unphysical values and locally corrects the solution on the marked cells. It is applied to the DG solution to a standard benchmark problem and compared to classical slope limiters.

Host
WIAS Berlin
Monday, 10.07.2023, 14:00 (Online Event)
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Patrick Jaap, WIAS:
A semismooth Newton solver with automatic differentiation written in C++ (online talk)
more ... Location
Online Event

Abstract
In this talk we consider problems of the form F(x)=0 where F is a nonlinear Newton differentiable mapping between Solbolev spaces. It is well-known that a semismooth Newton method ensures local superlinear convergence towards a solution. The function spaces are discretized by suitable finite elements over a given grid. A major difficulty is the practical implementation of generalized Jacobians. To this end, we present automatic differentiation techniques to obtain discrete subgradients of F. The resulting sparse linear problems are solved by efficient linear solvers. The framework is easy to use and to implement: The user only needs to implement a local evaluation of F in the weak form for a given set of test functions. An example implementation is given for a thermoforming model from a recent paper. To verify the solver, the results of this model are reproduced.

Further Informations
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations

Host
WIAS Berlin
Friday, 07.07.2023, 10:00 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Edriss S. Titi, University of Cambridge:
The inviscid primitive equations and the effect of fast rotation (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Large scale dynamics of the oceans and the atmosphere are governed by the primitive equation (PE). It is well-known that the three-dimensional viscous PE is globally well-posed in Sobolev spaces. In this talk, I will discuss the ill-posedness in Sobolev spaces, the local well-posedness in the space of analytic functions, and the finite-time blowup of solutions to the three-dimensional inviscid PE (also known as the hydrostatic Euler equations) with rotation (Coriolis force). Eventually, I will also show, in the case of “well-prepared" analytic initial data, the regularizing effect of the Coriolis force by providing a lower bound for the life-span of the solutions which grows toward infinity with the rotation rate. The latter is achieved by a delicate analysis of a simple limit resonant system whose solution approximates the corresponding solution of the 3D inviscid PE with the same initial data. In addition, and if time allows I will discuss Onsager's conjecture in the context of the inviscid primitive equations.

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Thursday, 06.07.2023, 12:15 (WIAS-405-406)
Seminar Interacting Random Systems
Naotaka Kajino, Kyoto University:
Two-sided bounds on tail probabilities of the number of collisions of random walks
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
I will consider two independent copies X^j=X^j_n_n, jin1,2, of a Markov chain X=X_n_n on a countable set V, and present the following result on the number T_n of collisions of X^1, X^2 up to time ninmathbbN defined by T_n:=sum_k=1^n1_X^1_k=X^2_k: If X is symmetric with respect to a measure mu on V which is comparable to the counting measure on V and satisfies the two-sided on-diagonal heat kernel bounds of strongly recurrent type, i.e., of spectral dimension 2alphain(0,2), then T_n satisfies a sharp two-sided stretched exponential bound on its upper tail probabilities, which in particular implies that T_n is typically of the order of n^1-alpha. This talk is based on a joint work with Kosei Konishi and Yukihiro Ushitaki.

Host
WIAS Berlin
Thursday, 06.07.2023, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Yuki Tokushige, The University of Manchester:
Scaling Limits of SRWs on the Long-Range Percolation Cluster
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
In this talk, we will discuss a Long-Range Percolation (LRP) on $mathbbZ^d$, which is a variant of the classical nearest-neighbor Bernoulli percolation. In particular, we consider a problem concerning a SRW on the infinite cluster of a LRP. In the paper published in 2013, Crawford and Sly proved that a SRW on the infinite cluster scales to $alpha$-stable process. However, they completed the proof only when $alphain(0, 1)$. It is because the remaining case involves a technical problem to do with a control of short jumps of a SRW, which is related to the fact that sample paths of $alpha$-stable process have infinite variations for $alphain[1, 2)$. In this talk, we will give a brief overview of this subject and explain our idea to overcome the technical issue depicted above and complete the proof of the case $alphain[1, 2)$. This talk is based on a joint work with Noam Berger (Technical University of Munich).

Host
WIAS Berlin
Tuesday, 04.07.2023, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Priv.-Doz. Dr. John G. M. Schoenmakers, WIAS Berlin:
Primal-dual regression approach for Markov decision processes with infinite state and action spaces (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Further Informations
Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Tuesday, 04.07.2023, 13:30 (WIAS-405-406)
Seminar Numerische Mathematik
Marwa Zainelabdeen, FU Berlin:
An optimally convergent convection-stabilized Taylor--Hood finite element method for the Oseen equations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
We consider the finite element discretization of the Oseen equations. The LSVS convection stabilization proposed in [1], which is motivated by the underlying vorticity equation has the advantage that it leads for the Scott--Vogelius finite element to a pressure-robust method. We extended the LSVS method to the classical Taylor--Hood finite element space which more flexible with respect to the computational grids and less costly due to a smaller pressure ansatz space. On the other hand it is not pressure-robust and does not satisfy the original assumptions for the LSVS convection stabilization. To improve the lack of pressure-robustness, the popular grad-div stabilization is added. A theoretical result in [2] stating that for large grad-div parameter gamma the Taylor- Hood method converges to the Scott--Vogelius method is carried over to the LSVS-grad-div stabilized scheme. In addition, by utilizing the already proved O(hk+ 12 ) Scott--Vogelius error estimate from [1], we proved an error estimate for the velocity of the same order for Taylor--Hood finite elements. Numerical studies are performed to test the method and investigate the optimal choice of the LSVS and the grad-div stabilization parameters.

Further Informations
References [1] N. Ahmed, G. R. Barrenechea, E. Burman, J. Guzman, A. Linke, C. Mer- don, A pressure-robust discretization of Oseen's equation using stabilization in the vorticity equation, SIAM J. Numer. Anal. 59(5), pp. 2746--2774, 2021 [2] M. A. Case, V. J. Ervin, A. Linke, L. G. Rebholz, A connection between Scott--Vogelius and grad-div stabilized Taylor--Hood FE approximations of the Navier--Stokes equations, SIAM J. Numer. Anal. 49(4), pp. 1461--1481, 2011

Host
WIAS Berlin
Tuesday, 04.07.2023, 10:15 (WIAS-HVP-3.04)
Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Dr. Guanghui Hu, Nankai University, China:
Time-harmonic scattering by periodic structures with Dirichlet and Neumann boundary conditions
more ... Location
Weierstraß-Institut, Hausvogteiplatz 11A, 10117 Berlin, 3. Etage, Raum: 3.04

Abstract
We consider well-posedness of TE and TM polarizations of time-harmonic electromagnetic scattering by perfectly conducting periodic surfaces and periodically arrayed obstacles. Inspired by recent studies on scattering by periodic dielectric layers, we propose a new radiation condition to characterize evanescent waves propagating along the scattering surface. Uniqueness and existence of time-harmonic scattering by incoming point source waves and plane waves from locally perturbed periodic structures are established under either the Dirichlet or Neumann boundary condition.

Host
WIAS Berlin
July 3 – 5, 2023 (WIAS-ESH)
Workshop/Konferenz: Nonlinear Dynamics in Semiconductor Lasers 2023
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
Ferdinand-Braun-Institut, Leibniz-Institut für Höchstfrequenztechnik
WIAS Berlin
Thursday, 29.06.2023, 14:00 (Online Event)
Seminar Numerische Mathematik
Sarah Katz, WIAS Berlin:
Impact of turbulence modeling on simulations of aortic blood flow
more ... Location
Online Event

Abstract
Due to the comparatively high flow rates at systole, blood flow in the aorta exhibits turbulent behavior. Simulations therefore require either very high spatial resolution or the use of a suitable turbulence model. This talk will present past work by RG3 in cooperation with the Charité's Institute of Computer-assisted Cardiovascular Medicine on the latter choice, comparing several relevant models, as well as an outlook on current efforts in applying machine learning to augment such simulations.

Further Informations
Numerics Seminar (FG3+LG5)

Host
WIAS Berlin
Wednesday, 28.06.2023, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Peter Lewintan, Universität Duisburg-Essen:
Optimal Korn--Maxwell--Sobolev inequalities (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We present a complete picture of coercive Korn-type inequalities for generalised incompatible fields, and optimally extend and unify several previously known inequalities that are crucial to the existence theory for a variety of models in continuum mechanics.

Further Informations
Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 28.06.2023, 14:00 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Peter Gladbach, Universität Bonn:
Homogenization and mean-field limits of transport costs (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We treat the limits, in terms of Gamma-convergence, of several discrete dynamic transport costs. The first concerns Wasserstein-type transport actions on stationary random graphs, for which we use stochastic homogenization and geometric measure theory to find a continuous limit functional. (joint work with Lorenzo Portinale and Jan Maas) The second treats interacting particles with different origins and destinations, which will develop coordinated oscillations in order to minimize a common functional. We show Gamma-convergence as the number of particles tends to infinity, and that minimizers converge to solutions of a Vlasov equation. (joint work with Bernhard Kepka)

Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 28.06.2023, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Céline Kerriou, Universität zu Köln:
Condensation in scale-free geometric graphs with excess edges
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
We identify the upper large deviation probability for the number of edges in scale-free geometric random graph models as the space volume goes to infinity. Our result covers the models of scale-free percolation and the Boolean model with heavy-tailed radius distribution and can be extended to various other models. In all these cases the mechanism behind the large deviation is based on a condensation effect for the vertex degrees. The mechanism randomly selects a finite number of vertices and increases their power, so that they connect to a macroscopic number of vertices in the graph, while the other vertices retain a degree close to their expectation and thus only make the expected contribution to the large deviation event.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Wednesday, 28.06.2023, 11:15 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Dr. Kartik Waghmare, École Polytechnique Fédérale de Lausanne, Schweiz:
Functional graphical lasso (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We consider the problem of recovering conditional independence relationships between p jointly distributed Hilbertian random elements given n realizations thereof. We operate in the sparse high-dimensional regime, where n << p and no element is related to more than d << p other elements. In this context, we propose an infinite-dimensional generalization of the graphical lasso. We prove model selection consistency under natural assumptions and extend many classical results to infinite dimensions. In particular, we do not require finite truncation or additional structural restrictions. The plug-in nature of our method makes it applicable to any observational regime, whether sparse or dense, and indifferent to serial dependence. Importantly, our method can be understood as naturally arising from a coherent maximum likelihood philosophy.

Further Informations
Der Vortrag findet auch via Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Wednesday, 28.06.2023, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Dr. Alessia Caponera, University of Milano-Bicocca, Italien:
Functional estimation of anisotropic covariance and autocovariance operators on the sphere (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In this talk we present nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a measurement framework where each random field among an identically distributed collection of spherical random fields is sampled at a few random directions, possibly subject to measurement error. The collection of random fields could be i.i.d. or serially dependent. Though similar setups have already been explored for random functions defined on the unit interval, the nonparametric estimators proposed in the literature often rely on local polynomials, which do not readily extend to the (product) spherical setting. We therefore formulate our estimation procedure as a variational problem involving a generalized Tikhonov regularization term. Using the machinery of reproducing kernel Hilbert spaces, we establish representer theorems that fully characterize the form of our estimators. We determine their uniform rates of convergence as the number of random fields diverges, both for the dense (increasing number of spatial samples) and sparse (bounded number of spatial samples) regimes. A preliminary exploration of climate data will also be discussed. This is based on joint works with Victor M. Panaretos, Julien Fageot, Matthieu Simeoni and Almond Stöcker.

Further Informations
Der Vortrag findet auch via Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Tuesday, 27.06.2023, 15:15 (FU-140)
Oberseminar Nonlinear Dynamics
Phillipo Lappicy, Freie Universität Berlin:
On the exceptional Bianchi models
more ... Location
Freie Universität Berlin, Arnimallee 7, 14195 Berlin, Hinterhaus, Raum: 140

Abstract
Most (if not all) rigorous results regarding spatially homogeneous and anisotropic cosmological singularities are based on the Bianchi types VIII and IX models, which constitute four-dimensional dynamical systems. However, there is one exceptional model which has the same dimensionality, but with almost no rigorous results: the Bianchi type VI-1/9 models. These exceptional models should play a distinguished role in the generic asymptotic dynamics towards cosmological singularities, especially when small spatial inhomogeneities are considered. We will discuss some early explorations/findings which are based on joint work with C. Uggla

Further Informations
Oberseminar Nonlinear Dynamics

Host
Freie Universität Berlin
WIAS Berlin
Tuesday, 27.06.2023, 15:15 (FU-140)
Oberseminar Nonlinear Dynamics
Prof. Jia-Yuan Dai, Freie Universität Berlin:
Exploring a new mechanism of periodic orbits: Dynamics of two predators competing for a prey
more ... Location
Freie Universität Berlin, Arnimallee 7, 14195 Berlin, Hinterhaus, Raum: 140

Abstract
We prove the existence of stable periodic orbits of an ODE system that describes the dynamics of two predators competing for the same prey. The prey population grows logistically in the absence of predation and the predators feed on the prey with Holling?s type-II nonlinearity. We explain how stable periodic orbits, located far away from the boundary planes, are triggered by perturbing an elliptic Hopf bifurcation point without parameters. To this end, we prove that the ODE system admits an elliptic Hopf bifurcation and the existence and stability of periodic orbits are ensured by the averaging method. This is a joint work with A. López Nieto, P. Lappicy, H. Stuke, and N. Vassena.

Further Informations
Oberseminar Nonlinear Dynamics

Host
Freie Universität Berlin
WIAS Berlin
Tuesday, 27.06.2023, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Prof. Dr. Vladimir Spokoiny, WIAS Berlin:
Sharp deviation bounds and concentration phenomenon for sub-gaussian quadratic forms (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
Under a mild assumption of linearity on the log-likelihood function, the tools of empirical processes are not necessary, the analysis of a general MLE can be reduced to a deviation bound for a quadratic form. This paper explains how the recent advances in Laplace approximation from [Spokoiny, 2022, 2023] can be used for obtaining sharp Gaussian-like finite sample bounds and for stating the prominent concentration phenomenon for the squared norm of a sub-gaussian vector. Some extensions and open problems will be discussed as well.

Further Informations
Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Thursday, 22.06.2023, 14:00 (WIAS-ESH)
Seminar Numerische Mathematik
Dr. Cristian Cárcamo Sánchez, WIAS Berlin:
A stabilized finite element method for the Stokes--Temperature coupled problem
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In this work, we introduce and analyze a new stabilized finite element scheme for the Stokes--Temperature coupled problem. This new scheme allows equal order of interpolation to approximate the quantities of interest, i.e. velocity, pressure, temperature, and stress. We analyze an equivalent variational formulation of the coupled problem inspired by the ideas proposed in [1]. The existence of the discrete solution is proved, decoupling the proposed stabilized scheme and using the help of continuous dependence results and Brouwer?s theorem under the standard assumption of sufficiently small data. Optimal convergence is proved under classic regularity assumptions of the solution. Finally, we present some numerical examples to show the quality of our scheme, in particular, we compare our results with those coming from a standard reference in geosciences described in [2].

Further Informations
References [1] M. Alvarez, G.N. Gatica, R. Ruiz?Baier, An augmented mixed-primal finite element method for a coupled flow-transport problem, ESAIM: M2AN 49 (2015) 1399?1427, https://doi.org/10.1051/m2an/2015015.. [2] P.E. van Keken, C. Currie, S.D. King, M.D. Behn, A. Cagnioncle, J. He, R.F. Katz, S.C. Lin, E.M. Parmentier, M. Spiegelman, K. Wang, A community bench- mark for subduction zone modeling, Phys. Earth Planet. Inter. 171 (2008) 187?197, https://doi.org/10.1016/j.pepi.2008.04.015.

Host
WIAS Berlin
Wednesday, 21.06.2023, 13:00 (WIAS-ESH)
Berlin Oberseminar: Optimization, Control and Inverse Problems
Dr. Leon Bungert, TU Berlin:
The geometry of adversarial machine learning
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
It is well-known that despite their aptness for complicated tasks like image classification, modern neural networks are prone to insusceptible input perturbations (a.k.a. adversarial attacks) which can lead to severe misclassifications. Adversarial training is a state-of-the-art method to train classifiers which are more robust against these adversarial attacks. The method features minimization of a robust risk and has interpretations as game-theoretic problem, distributionally robust optimization problem, dual of an optimal transport problem, or nonlocal geometric regularization problem. In this talk I will focus on the last interpretation which allows for the application of tools from calculus of variations and geometric measure theory to study existence, regularity, and asymptotic behavior of minimizers. In particular, I will show that adversarial training of binary agnostic classifiers is equivalent to a nonlocal and weighted perimeter regularization of the decision boundary. Furthermore, I will show Gamma-convergence of this perimeter to a local anisotropic perimeter as the strength of the adversary tends to zero, thereby establishing an asymptotic regularization effect of adversarial training. Lastly, I will discuss probabilistic relaxations of adversarial training which exhibit better clean accuracies and also have a perimeter-regularization interpretation.

Further Informations
Berlin Oberseminar: Optimization, Control and Inverse Problems

Host
WIAS Berlin
Technische Universität Berlin
Humboldt-Universität zu Berlin
Wednesday, 21.06.2023, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Sanjoy Jhawar, WIAS Berlin:
Moderate deviations in Poisson navigation
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
The content of this talk is a moderate deviation principle in random networks based on directed-navigations on the Poisson point process on the plane. In this navigation or routing scheme, starting from the origin, at each consecutive step a Poisson point is joined by an edge to its nearest Poisson point on the right. In these types of navigations the main problem is the dependency among the consecutive steps. The notion of distance in this model plays a key role in the analysis. In the case of the infinity norm, the problem is far easier to handle than the one in the case of the Euclidean norm, because of a natural independence among consecutive blocks of the navigation in the former situation. To use similar independence in the case of the Euclidean norm, instead we consider a cone of a certain angle (?) as the domain of exploration at each step, which makes the model a bit more restrictive but still rich from a modelling perspective. We call these models directed-navigation and directed-?-navigation respectively. The quantity of interest is the random variable for the deviation of the navigation path, starting from the origin, away from horizontal-axis and we establish a moderate deviation principle for this sequence of random variables. This is an ongoing work with Benedikt Jahnel.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Wednesday, 21.06.2023, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Dr. Eddie Aamari, Université Paris Diderot, Frankreich:
Minimax manifold estimation: Boundary, noise and computational constraints
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In this talk, we will present the optimal rates for the Hausdorff estimation of d-dimensional manifolds M in high ambient dimension. We will focus on the influence of the possible presence of a boundary dM on one hand, and on noise and computational constraints on the other hand. The studied geometric class of target manifolds that we consider reunites and extends the most prevalent C^2-type models: manifolds without boundary, and full-dimensional domains. A Voronoi-based procedure that allows to identify points close to dM will be presented. The noise and computational constraints will be addressed jointly through the statistical query (SQ) framework, which consists in replacing the usual access to samples from a distribution by the access to adversarially perturbed expected values of functions interactively chosen by the learner. This framework provides a natural estimation computational complexity measure, enforces robustness through adversariality, and is closely related to differential privacy. After presenting this framework in details, we will describe a purely geometric algorithm called Manifold Propagation, that reduces the problem to three local geometric routines: projection, tangent space estimation, and point detection. We will then provide constructions of these geometric routines in the SQ framework.

Further Informations
Der Vortrag findet auch via Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Tuesday, 20.06.2023, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Leon Bungert, TU Berlin:
Polarized consensus based particle dynamics (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
In this talk I will speak about a novel polarized consensus based method for optimization and sampling which relies on a kernelized weighted mean and covariance. This way the method allows for finding several global minima of non-convex functions and for multi-modal sampling. I will present numerical examples and first theoretical results on this novel method. This talk is based on recent joint work together with Tim Roith and Philipp Wacker.

Further Informations
Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Tuesday, 20.06.2023, 14:00 (WIAS-ESH)
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Dr. Evelyn Herberg, Heidelberg University:
Deep learning with variable time stepping (online talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Feature propagation in Deep Neural Networks (DNNs) can be associated to nonlinear discrete dynamical systems. The novelty, in this talk, lies in letting the discretization parameter (time step-size) vary from layer to layer, which needs to be learned, in an optimization framework. The proposed framework can be applied to any of the existing networks such as ResNet, DenseNet or Fractional-DNN. This framework is shown to help overcome the vanishing and exploding gradient issues. Stability of some of the existing continuous DNNs such as Fractional-DNN is also studied. The proposed approach is applied to an ill-posed 3D-Maxwell's equation.

Further Informations
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations

Host
WIAS Berlin
Thursday, 15.06.2023, 14:00 (WIAS-ESH)
Seminar Numerische Mathematik
Dr. Medine Demir, Weierstrass Institute:
Vorticity based stabilization method for fluid-fluid interaction problem
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Fluid-fluid interaction problem is of considerable interest especially in computational fluid dynamics simulations for different industrial and engineering applications. One of the common problem can be observed in atmosphere-ocean (AO) interactions. This work considers the approximate solutions of the two coupled fluid-fluid interaction problem in AO through nonlinear interface condition. In this study, we propose a different variant of SAV method essentially based on an effective VMS stabilization acts on only the small scales for the numerical simulation of the AO problem. Instead of using projection operator for VMS stabilization, the stabilization is dealt with vorticity term and grad-div stabilization in the viscous term. Geometric averaging will be used for decoupling. An important aspect of this consideration is not only conforming mixed finite element approximation is produced, but also with the use of vorticity extra storage requirement is reduced. In the case of small viscosity, the use of only three variables instead of nine variables enables to improve the solution of the system.

Host
WIAS Berlin
Wednesday, 14.06.2023, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Ass. Prof. Dr. Ana Leonor Silvestre, University of Lisbon, Portugal:
Optimal boundary control for the steady Navier--Stokes equations with directional do-nothing boundary conditions (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We consider the steady Navier--Stokes equations with mixed boundary conditions, where, instead of the classical do-nothing (CDN) outflow condition, a directional do-nothing (DDN) or a regularized directional do-nothing (RDDN) condition are imposed. An auxiliary reference flow, which will also work as a lifting of the inhomogeneous Dirichlet boundary values, is used to define the DDN and RDDN conditions. Our aim is the minimization of a cost functional of velocity tracking type by means of a control localized on the boundary. We prove the existence of a solution for this optimal control problem and, in the case of the RDDN condition, obtain the adjoint system and derive the corresponding first order optimality conditions. All results are obtained under appropriate assumptions on the size of the data and the controls, which, however, are less restrictive when compared with the case of a CDN outflow condition. This is a joint work with Pedro Nogueira and Jorge Tiago (IST, U Lisboa)

Further Informations
Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 13.06.2023, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Oleg Butkovsky, WIAS Berlin:
Stochastic sewing for weak uniqueness of SDEs and SPDEs (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
I would like to report about very early steps of a new project. It has been thought for a while that stochastic sewing is relevant only for obtaining strong unqiueness and strong rate of convergence of numerical methods. I will try to convince you that stochastic sewing combined with the Scheutzow-Kulik generalized coupling technique allows to achieve weak uniqueness of SDEs and weak rate of convergence of Euler scheme. Work in progress with Leonid Mytnik.

Further Informations
Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Wednesday, 07.06.2023, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Günter Last, Karlsruher Institut für Technologie:
A Palm approach to tail processes and tail measures
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
Tail processes and tail measures are important concepts in the theory of regularly varying (heavy tailed) time series. In this talk we will show that these concepts are intimately related to Palm theory of stationary random measures. To motivate the topic, we start with providing some background on regularly varying time series. Then we shall introduce tail fields in an intrinsic way, namely as spectrally decomposable random fields satisfying a certain space shift formula. The index set is allowed to be a general locally compact Hausdorff Abelian group. The field may take its values in an Euclidean space or even in an arbitrary measurable cone, equipped with a pseudo norm. We characterize mass-stationarity of the exceedance random measure in terms of a suitable version of the classical Mecke equation. As a rule, the associated stationary measure is not finite. We shall show that it is homogeneous, that is a tail measure. Finally we will establish a spectral representation of stationary tail measures. The talk is based on our recent work arXiv:2112.15380.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Tuesday, 06.06.2023, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Simon Breneis, WIAS Berlin:
American options under rough Heston (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
The rough Heston model is a popular option pricing model in mathematical finance. However, due to the non-semimartingale and non-Markovian characteristics of its volatility process, simulations can be prohibitively expensive in practice. Building on previous works, we approximate the volatility process with an N-dimensional diffusion, yielding a Markovian approximation of the rough Heston model. Then, we introduce a weak discretization scheme to simulate paths of these Markovian approximations. Our numerical experiments show that these approximations converge at a second-order rate as the number of time steps approaches infinity. We leverage these approximations to price American options under the rough Heston model.

Further Informations
Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Thursday, 01.06.2023, 14:00 (WIAS-ESH)
Forschungsseminar Mathematische Modelle der Photonik
Lasse Ermoneit, WIAS:
Simulation of single-electron shuttling in a SiGe quantum bus
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Forschungsseminar Mathematische Modelle der Photonik

Host
WIAS Berlin
Wednesday, 31.05.2023, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Dr. Randolf Altmeyer, University of Cambridge:
Statistics for stochastic PDEs: Optimal rates and a nonparametric LAN expansion (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We consider the problem of estimating the coefficients in second order linear stochastic partial differential equations (SPDE) from spatially discrete or locally averaged observations on a finite time horizon. For a nonparametric diffusivity, we obtain the local asymptotic normality (LAN) property, opening up the road to efficient estimation. The proof reveals interesting aspects of partially observed space-time random fields. It relies on stochastic filtering techniques, on the reproducing kernel Hilbert space of the observation process as well as on the solution of certain Wiener-Hopf integral equations. For lower order terms, we obtain rate-optimal estimators, exhibiting different rates of convergence depending on the differential order. We further establish a general moment-based technique for the joint estimation of diffusivity and volatility parameters, covering both discrete and local measurements.

Further Informations
Der Vortrag findet auch via Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Friday, 26.05.2023, 13:00 (WIAS-Library)
E-Coffee-Lecture
Dr. Timo Streckenbach, WIAS:
AI-based programming
more ... Location
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411

Host
WIAS Berlin
Thursday, 25.05.2023, 16:00 (FUB-025 026)
Oberseminar Nonlinear Dynamics
Dr. Isabelle Schneider:
From Pythagoras to differential equations: Uncovering the mysteries of musical sound
more ... Location
Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Erdgeschoss, Raum: 025/026

Abstract
For over two millennia, the relationship between the frequency of a vibrating string monochord. Many renowned scientists and mathematicians, including Mersenne, Bernoulli, Euler, Lagrange, d' Alembert, and Helmholtz, have conducted their own investigations on this subject. Despite the fact that the linear wave equation is frequently employed to model the sound spectrum of musical instruments, it does not truly reproduce the entire sound spectrum. In this talk, we will embark on a search for the flageolet harmonics and compare our mathematical findings to what we hear during live musical experiments. We will investigate recent models for string and woodwind instruments that rely on partial and delay differential equations, and we will uncover intriguing phenomena such as stiff damping and hysteresis.

Host
Freie Universität Berlin
WIAS Berlin
Thursday, 25.05.2023, 14:00 (WIAS-ESH)
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Dr. Brendan Keith, Brown University, USA:
The entropic finite element method
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
One of the longest-standing challenges in finite element analysis is to develop a stable, high-order Galerkin method that strictly enforces pointwise bound constraints. The entropic finite element method (EFEM) is a nonlinear, structure-preserving method with these properties. This talk will introduce EFEM and describe its capability for treating free-boundary problems, enforcing discrete maximum principles, and designing scalable, mesh-independent algorithms for inverse design problems. The overall methodology combines ideas from nonlinear programming, functional analysis, and differential geometry and can potentially lead to new synergies among these areas.

Further Informations
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization

Host
WIAS Berlin
Wednesday, 24.05.2023, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Pavel Krejči, Czech Technical University in Prague, Tschechische Republik:
Degenerate hysteresis in partially saturated porous media (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We propose a model for fluid diffusion in partially saturated porous media taking into account hysteresis effects in the pressure-saturation relation. The resulting mathematical problem leads to a diffusion equation with Robin boundary condition for the pressure in an N-dimensional domain with a Preisach hysteresis operator under the time derivative. The problem is doubly degenerate in the sense that the saturation range is bounded, and no a priori control of the time derivative of the pressure is available. A bootstrapping argument based on particular geometric properties of the hysteresis operator makes it possible to prove the existence and uniqueness of a strong solution to the problem for arbitrarily large data. This is a joint work with Chiara Gavioli from TU Wien.

Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 24.05.2023, 14:00 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Abramo Agosti, Università Pavia, Italy:
A Cahn--Hilliard phase field model coupled to viscoelasticity at large strains (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In this talk I will present a new Cahn--Hilliard phase field model coupled to incompressible viscoelasticity at large strains, obtained from a diffuse interface mixture model and formulated in the Eulerian configuration. The free energy density of the system is given as the sum of a Cahn--Hilliard term and an elastic term, with a coupling between the phase field variable and the elastic deformation gradient in the elastic contribution. I will introduce different kinds of diffusive regularizations of the transport equation for the deformation gradient, and I will discuss the proof of the global existence of weak solutions in three space dimensions for the regularized system with generic nonlinear elastic energy densities with polynomial growth, comprising the relevant cases of polyconvex Mooney--Rivlin and Ogden elastic energies. I will also propose two kinds of well posed and unconditionally energy stable finite element approximations of the model, based on convex splitting ideas and on the use of a scalar auxiliary variable. Finally, I will show numerical results for different test cases with shape memory alloy type free energy, and I will discuss some possible applications and future developments of the model in the field of biomathematical modeling for computational medicine.

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 24.05.2023, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Renato Soares dos Santos, Universidade Federal de Minas Gerais (UFMG), Brasilien:
Ballistic random walk on the zero-range process
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
We consider a random walk on a dynamic random environment given by a zero-range process started from equilibrium. Assuming that the random walk is ballistic with a large enough speed, we obtain a law of large numbers for the position of the random walk. The proof is based on renormalization arguments and decoupling inequalities without appealing to renewal schemes. Joint work with Weberson Arcanjo, Rangel Baldasso and Marcelo Hilário.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Wednesday, 24.05.2023, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Dr Jonathan Niles-Weed, New York University, USA:
Optimal transport map estimation in general function spaces (online talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Optimal transport map estimation in general function spaces (online talk) We consider the problem of estimating the optimal transport map between a (fixed) source distribution P and an unknown target distribution Q, based on samples from Q. The estimation of such optimal transport maps has become increasingly relevant in modern statistical applications, such as generative modeling. At present, estimation rates are only known in a few settings (e.g. when P and Q have densities bounded above and below and when the transport map lies in a Hölder class), which are often not reflected in practice. We present a unified methodology for obtaining rates of estimation of optimal transport maps in general function spaces. Our assumptions are significantly weaker than those appearing in the literature: we require only that the source measure P satisfies a Poincaré inequality and that the optimal map be the gradient of a smooth convex function that lies in a space whose metric entropy can be controlled. As a special case, we recover known estimation rates for bounded densities and Hölder transport maps, but also obtain nearly sharp results in many settings not covered by prior work. For example, we provide the first statistical rates of estimation when P is the normal distribution and the transport map is given by an infinite-width shallow neural network. Joint work with Divol and Pooladian.

Further Informations
Der Vortrag findet via Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Tuesday, 23.05.2023, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Prof. Dr. Daniel Walter, Humboldt Universität zu Berlin:
Nonsmooth minimization in infinite dimensional spaces meets sparse dictionary learning (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
We propose a novel method for problems involving nonsmooth but convex regularization terms over infinite dimensional function spaces . It resembles a dictionary learning algorithm which switches between the update of a dictionary $mathcalA_k$ of extremal points of the unit ball of the regularizer and of a sparse represenation of the iterate $u_k$ in its conic hull by solving a finite dimensional $ell_1$-regularized problem. Imposing additional assumptions on the involved dual variables , its asymptotic linear convergence is shown. The theoretical results are accompanied by numerical experiments involving challenging regularizers such as the Benamou-Brenier energy as well as the BV-seminorm, highlighting both, the sharpeness of our results as well as the practical applicability of the method.

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Wednesday, 17.05.2023, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Willem van Oosterhout, WIAS Berlin:
Analysis of poro-visco-elastic solids at finite strains (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Poro-visco-elastic solids are materials in which a species diffuses and contributes to their deformation. Taking the Biot model as starting point, we discuss the modelling of (large) deformations and diffusion processes in a physically consistent way, and show that under certain assumptions weak solutions exist. To model poro-visco-elastic materials, a free energy functional and dissipation potential are introduced. This energy functional has contributions both from the deformation gradient, i.e., an elastic contribution, and from a mixing term, which couples the deformation gradient and the concentration of the species. The dissipation potential features contributions for the viscous evolution and the diffusion process. In particular, since the focus is on finite-strain elasticity, the diffusion equation has to be pulled back to the reference configuration. As the pulledback mobility tensor depends nonlinearly on the deformation gradient, and the viscous stresses are frame-indifferent, it is analytically necessary to include the hyperstress as a higher-order regularization, which makes this a second order non-simple material. Another important property of the investigated model is that it allows for degenerate mobilities, which are more physically relevant; however, this greatly complicates the analysis, and requires an additional regularization step. This is in contrast to prior work, where only nondegenerate mobilities were considered. Still, under certain assumptions on the constitutive laws and the data, the existence of weak solutions to the coupled system is shown using variational methods. This is joint work with Matthias Liero.

Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 17.05.2023, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Clément Erignoux, INRIA Lille, Frankreich:
Symmetric and asymmetric hydrodynamics for the facilitated exclusion process via mapping
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
The facilitated exclusion process is a degenerate kinetically constrained lattice gas, in which particles can hop to an empty neighboring site provided that another neighboring site is also occupied. Because of the kinetic constraint, the system in dimension 1 exhibits two phases, a frozen phase at density less than 1/2, and a diffusive phase at density larger than 1/2. For this reason, standard entropic tools cannot be used to straightforwardly derive its macroscopic behavior, in particular its hydrodynamic limit. To workaround this issue, we exploit a classical mapping between exclusion and zero-range processes, and deduce from the hydrodynamic limit of the zero-range process that of the exclusion process. Despite the lack of smoothness of the various macroscopic limits, thanks to the attractiveness of the zero-range process, this allows to derive the hydrodynamic limits in both the symmetric and asymmetric case. Based on JW With O. Blondel, M. Sasada, M. Simon and L. Zhao

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Wednesday, 17.05.2023, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. Dr. Enno Mammen, Universität Heidelberg:
Random planted forest: A directly interpretable tree ensemble (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We introduce a novel interpretable, tree based algorithm for prediction in a regression setting in which each tree in a classical random forest is replaced by a family of planted trees that grow simultaneously. The motivation for our algorithm is to estimate the unknown regression function from a functional ANOVA decomposition perspective, where each tree corresponds to a function within that decomposition. Therefore, planted trees are limited in the number of interaction terms. The maximal order of approximation in the ANOVA decomposition can be specified or left unlimited. If a first order approximation is chosen, the result is an additive model. In the other extreme case, if the order of approximation is not limited, the resulting model places no restrictions on the form of the regression function. The talk reports on joint work with Munir Hiabu and Joseph T. Meyer.

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Tuesday, 16.05.2023, 15:15 (WIAS-ESH)
Seminar Materialmodellierung
Prof. Dr. Amit Acharya, Carnegie Mellon University, USA:
Slow time-scale behavior of fast microscopic dynamics (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
This talk aims to understand and exploit the slow time-scale behavior of rapidly evolving microscopic dynamics posed in terms of systems of nonlinear ordinary differential equations, not necessarily containing an a priori split into fast and slow variables. Such a question arises naturally and ubiquitously in efforts to understand macroscopic dynamics, on engineering time-scales, of well-accepted models of microscopic dynamics that, however, are not amenable to practical computing over the much, much larger macroscopic time-scales of interest. This is because there is a vast separation of time scales involved between the dynamics of the macroscopic variables of interest and the microscopic dynamics, and evolving the microscopic dynamics directly fails to address the question of the macroscopic dynamics. The methodology employed involves a computational scheme based on fundamental mathematical theory that a) defines appropriate `coarse' variables corresponding to the microscopic dynamics that evolve in a stable manner on the coarse time scale; b) determines the equation of evolution for such variables; and c) defines a practically useful strategy for accurately initializing short bursts of microscopic runs for the evolution of the slow variables, without special requirements on the nature of the microscopic dynamics. We will illustrate the theory with examples that violate ergodicity and include both conservative and dissipative behavior. A first step towards coarse graining of discrete dislocation dynamics to a pde-based plasticity model without relying on constitutive assumptions will also be demonstrated. This is joint work with Sabyasachi Chatterjee, Zvi Artstein, Giacomo Po, Xiaohan Zhang, and Nasr Ghoniem.

Further Informations
Seminar Materialmodellierung

Host
WIAS Berlin
Tuesday, 16.05.2023, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Christian Bayer, WIAS Berlin:
An introduction to Hawkes processes (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
Hawkes processes are a prototypical example of self-exciting point processes. They are one of the most useful processes in science, engineering, and finance. Introduced as a model for time and magnitude of earthquakes, they have also been used as models for epidemics, crimes, traffic accidents, and so on. In finance, they are often used as models for order flow, for instance in order to solve the optimal execution problem, or to analyse market activity. We give a short introduction into Hawkes processes, including motivation, definitions and basic properties, and simulation.

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Tuesday, 16.05.2023, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Christian Hirsch, Aarhus University, Dänemark:
On the topology of higher-order age-dependent random connection models
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
On the topology of higher-order age-dependent random connection models Abstract: Preferential attachment is a popular mechanism for generating scale-free networks. While it offers a compelling narrative, the underlying reinforced processes make it difficult to rigorously establish subtle properties. Recently, age-dependent random connection models were proposed as an alternative that is capable of generating similar networks with a mechanism that is amenable to a more refined analysis. In this talk, we analyze the asymptotic behavior of higher-order topological characteristics such as higher-order degree distributions and Betti numbers in large domains. This talk is based on joint work with Péter Juhász.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Monday, 15.05.2023, 10:30 (WIAS-405-406)
Seminar Interacting Random Systems
Julian Kern, WIAS Berlin:
Mini Course: A unified approach to non-gradient systems (part 3)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
Recently, Makiko Sasada has published a trilogy of papers analyzing proofs for hydrodynamic limits in the context of non-gradient systems. The breakthrough lies in a conceptual change, realizing that it is useful to study the geometric properties of a system independently of the stochastic data. So far, all proofs relied on the specific structure of the underlying model. Using methods from cohomology of groups, Sasada is able to provide a unified approach to a large class of models. The aim of this Mini Course is to provide an introduction to her ideas as well as a basis for further discussion. Background: Some algebra; it might be useful to attend the presentation on May 9 as the mini course concentrates exclusively on the difficult part of the non-gradient method. Literature: "Topological Structures of Large Scale Interacting Systems via Uniform Functions and Forms", Ä Decomposition Theorem of Varadhan Type for Closed Co-Local Forms", "Varadhan's Decomposition of Shift-Invariant Closed L2-forms for Large Scale Interacting Systems on the Euclidean Lattice".

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Friday, 12.05.2023, 10:30 (WIAS-405-406)
Seminar Interacting Random Systems
Julian Kern, WIAS Berlin:
Mini Course: A unified approach to non-gradient systems (part 2)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
Recently, Makiko Sasada has published a trilogy of papers analyzing proofs for hydrodynamic limits in the context of non-gradient systems. The breakthrough lies in a conceptual change, realizing that it is useful to study the geometric properties of a system independently of the stochastic data. So far, all proofs relied on the specific structure of the underlying model. Using methods from cohomology of groups, Sasada is able to provide a unified approach to a large class of models. The aim of this Mini Course is to provide an introduction to her ideas as well as a basis for further discussion. Background: Some algebra; it might be useful to attend the presentation on May 9 as the mini course concentrates exclusively on the difficult part of the non-gradient method. Literature: "Topological Structures of Large Scale Interacting Systems via Uniform Functions and Forms", Ä Decomposition Theorem of Varadhan Type for Closed Co-Local Forms", "Varadhan's Decomposition of Shift-Invariant Closed L2-forms for Large Scale Interacting Systems on the Euclidean Lattice".

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Thursday, 11.05.2023, 10:30 (WIAS-405-406)
Seminar Interacting Random Systems
Julian Kern, WIAS Berlin:
Mini Course: A unified approach to non-gradient systems (part 1)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
Recently, Makiko Sasada has published a trilogy of papers analyzing proofs for hydrodynamic limits in the context of non-gradient systems. The breakthrough lies in a conceptual change, realizing that it is useful to study the geometric properties of a system independently of the stochastic data. So far, all proofs relied on the specific structure of the underlying model. Using methods from cohomology of groups, Sasada is able to provide a unified approach to a large class of models. The aim of this Mini Course is to provide an introduction to her ideas as well as a basis for further discussion. Background: Some algebra; it might be useful to attend the presentation on May 9 as the mini course concentrates exclusively on the difficult part of the non-gradient method. Literature: "Topological Structures of Large Scale Interacting Systems via Uniform Functions and Forms", Ä Decomposition Theorem of Varadhan Type for Closed Co-Local Forms", "Varadhan's Decomposition of Shift-Invariant Closed L2-forms for Large Scale Interacting Systems on the Euclidean Lattice".

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
May 10 – 12, 2023 (WIAS-ESH)
Workshop/Konferenz: Frontiers of Stochastic Optimization and its Applications in Industry
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin
Tuesday, 09.05.2023, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Julian Kern, WIAS Berlin:
The crux of the non-gradient method
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
Most particle systems that have been studied so far have a so-called gradient property. However, the gradient property seems to be very special and only few systems exhibit it. Unfortunately, non-gradient systems prove to be much harder to analyze. The aim of this talk is to introduce the ideas for proving a hydrodynamic limit (= law of large numbers) for a non-gradient system. Focus is on the structure of the proof. In particular, we will identify which part of the proof becomes much more difficult without the gradient property.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Thursday, 04.05.2023, 14:00 (WIAS-ESH)
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Prof. Dr. Eskil Hansen, Lund University, Sweden:
Convergence analysis of the nonoverlapping Robin-Robin method for nonlinear elliptic equations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
The nonoverlapping Robin-Robin method is commonly encountered when discretizing elliptic equations, as it enables the usage of parallel and distributed hardware. Convergence has been derived in various linear contexts, but little has been proven for nonlinear equations. In this talk we present a convergence analysis for the Robin-Robin method applied to nonlinear elliptic equations with a p-structure, including degenerate diffusion equations governed by the p-Laplacian. The analysis relies on a new theory for nonlinear Steklov-Poincare operators based on the p-structure and the Lp-generalization of the Lions-Magenes spaces. This framework allows the reformulation of the Robin-Robin method into a Peaceman-Rachford splitting on the interfaces of the subdomains, and the convergence analysis then follows by employing elements of the abstract theory for monotone operators. This is joint work with Emil Engström (Lund University)

Further Informations
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization

Host
WIAS Berlin
Wednesday, 03.05.2023, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
PD Dr. Matthias Liero, WIAS Berlin:
Geodesic convexity in the Hellinger-Kantorovich space (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 03.05.2023, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Luisa Andreis, Politecnico di Milano, Italien:
Rare events for sparse random graphs and some new large deviation result
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
Rare events for dense random graphs are well described using the theory of large deviations and graphons. When graphs are sparse the picture is less clear, objects that describe globally the graphs and their limits, as graphons do for dense graphs, have not been defined yet. Nevertheless we do have information on how these graphs look like when explored locally from a vertex and this, under some assumptions, gives also information on global properties. In this talk I will give an overview on what is known for rare events in this regime, and I will present some recent new results, in particular on uniform graphs with a given degree. This talk is partially based on ongoing joint work with B. Chin, M. Dickson, S. Donderwinkel, R. van der Hofstad and N. Malhotra.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Wednesday, 03.05.2023, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. Dr. Gilles Blanchard, Université Paris Saclay, Frankreich:
Stein effect for estimating many vector means: A "blessing of dimensionality" phenomenon (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Consider the problem of joint estimation of the means for a large number of distributions in R^d using separate, independent data sets from each of them, sometimes also called "multi-task averaging" problem. We propose an improved estimator (compared to the naive empirical means of each data set) to exploit possible similarities between means, without any related information being known in advance. The idea is to shrink each mean towards a convex combination of its neighbors (determined by testing). We prove that this approach provides an improvement in mean squared error that can be quite significant when the (effective) dimensionality of the data is large, and when the unknown means exhibit structure such as clustering or concentration on a low-dimensional set (but which is totally unknown in advance). This is directly linked to the fact that the separation distance for testing is smaller than the estimation error in high dimension and generalizes the well-known James-Stein phenomenon. An application of this approach is the estimation of multiple kernel mean embeddings, which plays an important role in many modern applications. (This is based on joined work with Hannah Marienwald and Jean-Baptiste Fermanian)

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Friday, 28.04.2023, 13:00 (WIAS-Library)
E-Coffee-Lecture
Dr. Jürgen Fuhrmann, WIAS:
Some cool and (more or less) new tools for Unix and others: pandoc, rg, fzf, gitui
more ... Location
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411

Abstract
Where is my file ? How do I convert my markdown text to LaTeX ? What was the name of the file where I wrote that phrase ? How can I keep track of my git repository ? Stay up-to-date with tools written in Haskell, Rust an Go which complement the classical UNIX command line canon.

Further Informations
Hybrid event

Host
WIAS Berlin
April 27 – 29, 2023 (WIAS-ESH)
Workshop/Konferenz: 17th Annual Berlin-Oxford Young Researchers Meeting on Applied Stochastic Analysis
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
Technische Universität Berlin
University of Oxford
WIAS Berlin
Wednesday, 26.04.2023, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Pierluigi Colli, Università di Pavia, Italien:
The Cahn--Hilliard--Oono system with control in the mass term (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
The problem of optimal control for the Cahn--Hilliard--Oono system is addressed, where the control u is located in the mass term. First, well-posedness of the problem and the dependence of the phase variable on the control u are considered, all this by admitting general potentials that include both the case of regular potentials and the case of some singular potential. Next, the so-called separation property is discussed: it holds for everywhere defined regular potentials in 2D and 3D and for the logarithmic potential in 2D. Finally, in this framework, for the control problem it is shown that an optimal control exists; the control-to-state map is Frechet differentiable; a proper variational inequality involving the solution of an adjoint system is a necessary condition for optimality. The results reported in this talk have been obtained in a collaboration with G. Gilardi, E. Rocca and J. Sprekels.

Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 26.04.2023, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Heide Langhammer, WIAS Berlin:
LDP for the particle statistics in a spatial coagulation process
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
We introduce an interacting particle system for spatial coagulation. The process that we consider starts with N particles that each have a location in a compact space and a mass that is initially equal to one. In a coagulation event two particles with positions x and x' and masses m and m' merge and form a new particle that has mass m+m' and a new location. Exponential clocks determine the next coagulation event. They run independently for each pair of particles with a rate K(x,m,x', m') depending on the properties of the particle pair. We derive a formula for the distribution of the particle configuration after a fixed time T>0 and use it as a starting point to derive a large deviations principle. The formula is obtained by identifying each particle present at time T with a binary tree that encodes the coagulation history of the particle. Indeed, we can think of the system of particles as the outcome of a Poisson point process that randomly generates trees and whose distribution is transformed by an exponential density that contains the cost of keeping each pair of trees separated up to time T. The talk is based on joint work with Luisa Andreis, Wolfgang König and Robert Patterson.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Wednesday, 26.04.2023, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. Dr. Vladimir Spokoiny, WIAS Berlin:
Estimation and inference for Error-on-Operator models (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Many statistical models can be considered as particular cases of the Error-in-Operator (EiO) model. The list includes high dimensional random design regression, instrumental variables and error-in-variables regression, stochastic diffusion and interacting particle systems models among many others. The talk focuses on theoretical guarantees for the EiO model for finite samples using general theory of semiparametric estimation combined with the recent progress for stochastically linear models.

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Tuesday, 25.04.2023, 15:00 (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Sven Wang, Massachusetts Institute of Technology:
On polynomial-time mixing of MCMC for high-dimensional posterior distributions (online talk)
more ... Location
Online Event

Abstract
We consider the problem of generating random samples from high-dimensional posterior distributions. We will discuss both (i) conditions under which diffusion-based MCMC algorithms mix in polynomial-time (based on https://arxiv.org/pdf/2009.05298.pdf) as well as (ii) situations in which MCMC suffers from an exponentially long mixing time (based on https://arxiv.org/pdf/2209.02001.pdf). We will focus on the setting of non-linear inverse regression models. Our positive results on polynomial-time mixing are derived under local `gradient stability' assumptions on the forward map, which can be verified for a range of well-known non-linear inverse problems involving elliptic PDE, as well as under the assumption that a good initializer is available. Our negative results on exponentially long mixing times hold for `cold-start' MCMC. We show that there exist non-linear regression models in which the posterior distribution is unimodal, but there exists a so-called `free entropy barrier', which local Markov chains take an exponentially long time to traverse.

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Wednesday, 19.04.2023, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Leon Schütz, WIAS Berlin:
An existence theory for solitary waves on a ferrofluid jet (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 19.04.2023, 14:00 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Daniel Hauer, The University of Sidney, Australien:
The fundamental gap conjecture (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 19.04.2023, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Tejas Iyer, WIAS Berlin:
Properties of recursive trees with independent fitnesses
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
We study a general model of recursive trees, where nodes are equipped with random weights, arrive one at a time, and connect to existing nodes with probability proportional to a general function of their degree and their weight. We study the limiting infinite tree associated with this model, and show that, under a certain 'explosive' regime, the limiting tree has only a single node of infinite degree, or a single infinite path. We provide sufficient criteria to determine which occurs. Based, in part, on joint work with Bas Lodewijks.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Wednesday, 19.04.2023, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Dr. Chen Huang, Aarhus University, Dänemark:
Arellano-Bond LASSO estimator for long panel dynamic linear models (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Tuesday, 18.04.2023, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Wilfried Kenmoe Nzali, WIAS Berlin:
Optimal control problem in energy finance (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
April 17 – 19, 2023 (ATB Potsdam)
Workshop/Konferenz: Leibniz MMS Days 2023
more ... Location
Leibniz Institute for Agricultural Engineering and Bioeconomy Potsdam (ATB)

Host
Leibniz Institute for Agricultural Engineering and Bioeconomy
WIAS Berlin
Tuesday, 11.04.2023, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Alexandra Suvorikova, WIAS Berlin:
Data ordering in general metric spaces (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Further Informations
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics

Host
WIAS Berlin
Thursday, 06.04.2023, 11:00 (WIAS-ESH)
Seminar Materialmodellierung
Dr. Markus Mittnenzweig, Weizmann Institute of Science, Israel:
From an egg to an embryo - Inferring the temporal dynamics of cells during embryonic development (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Novel single-genomics technologies allow probing biological tissues and entire embryos at unprecedented molecular resolution. In the context of developmental biology, these technologies allow measuring in a very quantitative way the emergence of spatial and molecular complexity that characterizes early embryonic development. Mouse embryonic development is a canonical model for studying mammalian cell fate acquisition. Recently, we introduced a temporal flow model for early mouse development, consisting of data from 153 individually sampled embryos spanning 36 hours of molecular diversification. Using a convex optimization framework and precise timing of embryos we infer the differentiation dynamics of individual cells along the continuum of embryonic cellular states. In the second part, I will show how to use this time-resolved model to assess the function of epigenetic regulators and intercellular signals involved in early embryonic development.

Further Informations
Seminar Materialmodellierung

Host
WIAS Berlin
Tuesday, 04.04.2023, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Robert A. Vandermeulen, TU Berlin:
Beating the nonparametric curse of dimensionality using multi-view density estimators (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
The curse of dimensionality is a famous statistical phenomenon that is perhaps nowhere better exemplified than in the task of nonparametric density estimation. Here the curse of dimensionality is not only evident in practical applications, but there is a very robust corpus of theoretical work that demonstrate the curse of dimensionality. This talk will cover recent work on nonparametric density estimation that utilizes multi-view models, which are a type of low-rank model, to obviate the curse of dimensionality and give dimension-independent rates of convergence.

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Tuesday, 28.03.2023, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Luca Pelizzari, WIAS Berlin:
Primal-dual optimal stopping with signatures
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Further Informations
Hybrid event. Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Friday, 24.03.2023, 13:00 (WIAS-Library)
E-Coffee-Lecture
Heike Sill, WIAS:
Kosten-Leistungs-Rechnung (KLR) am WIAS
more ... Location
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411

Further Informations
hybrid event

Host
WIAS Berlin
Thursday, 23.03.2023, 16:00 (WIAS-ESH)
Forschungsseminar Mathematische Modelle der Photonik
Lutz Mertenskötter, WIAS Berlin:
Laser linewidth estimation beyond the detector noise limit - Statistical inference from delayed self-heterodyne measurements
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Forschungsseminar Mathematische Modelle der Photonik

Host
WIAS Berlin
Thursday, 23.03.2023, 14:00 (WIAS-ESH)
Seminar Numerische Mathematik
Dr. Gabriel R. Barrenechea, University of Strathclyde, UK:
Positivity-preserving discretisations in general meshes
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
The quest for physical consistency in the discretisation of PDEs started as soon as the numerical methods started being proposed. By physical consistency we mean a discretisation that by design satisfies a property also satisfied by the continuous PDE. This property might be positivity of the discrete solution, or preservation of some bounds (e.g., concentrations should belong to the interval [0, 1]), or can also be energy preservation, or exactly divergence-free velocities for incompressible fluids. Regarding positivity preservation, this topic has been around since the pioneering work by Ph. Ciarlet in the late 1960s and early 1970s. In the context of finite element methods, it was shown in those early works (and not significantly improved since), that in order for a finite element method to preserve positivity the mesh needs to satisfy certain geometrical restrictions, e.g., in two space dimensions with simplicial elements the triangulation needs to be of Delaunay type (in higher dimensions or quadrilateral meshes the restrictions are more involved). Throughout the years several conclusions have been reached in this topic, but in the context of finite element methods the discretisations tend to be of first order in space. So, many important problems still remain open. In particular, one open problem is how to build a discretisation that will lead to a positive solution regardless of the geometry of the mesh and the order of the finite element method. In this talk I will review recent results addressing the last question posed in the last paragraph. More precisely, I will present a method that enforces bound-preservation (at the degrees of freedom) of the discrete solution. The method is built by first defining an algebraic projection onto the convex closed set of finite element functions that satisfy the bounds given by the solution of the PDE. Then, this projection is hardwired into the definition of the method by writing a discrete problem posed for this projected part of the solution. Since this process is done independently of the shape of the basis functions, and no result on the resulting finite element matrix is used, then the outcome is a finite element function that satisfies the bounds at the degrees of freedom. Another important observation to make is that this approach is related to variational inequalities, and this fact will be exploited in the error analysis. The core of the talk will be devoted to explaining the main idea in the context of linear (and nonlinear) reaction-diffusion equations. Then, I will explain the main difficulties encountered when extending this method to convection-diffusion equations, and, more importantly, to a finite element method defined in polytopal meshes. The results in this talk have been carried out in collaboration with Abdolreza Amiri (Strathclyde, UK), Emmanuil Geourgoulis (Heriot-Watt, UK and Athens, Greece), Tristan Pryer (Bath, UK), and Andreas Veeser (Milan, Italy).

Further Informations
Seminar Numerische Mathematik

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 22.03.2023, 10:00 (WIAS-406)
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Dr. Constantin Christof, Technische Universität München:
On the identification and optimization of nonsmooth superposition operators in semilinear elliptic PDEs
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
We study an infinite-dimensional optimization problem that aims to identify the Nemytskii operator in the nonlinear part of a prototypical semilinear elliptic partial differential equation which minimizes the distance between the PDE-solution and a given desired state. In contrast to previous works, we consider this identification problem in a low-regularity regime in which the function inducing the Nemytskii operator is a-priori only known to be an element of H1loc. This makes the studied problem class a suitable point of departure for the rigorous analysis of training problems for learning-informed PDEs in which an unknown superposition operator is approximated by means of a neural network with nonsmooth activation functions (ReLU, leaky-ReLU, etc.). We establish that, despite the low regularity of the controls, it is possible to derive a classical stationarity system for local minimizers and to solve the considered problem by means of a gradient projection method. It is also shown that the established first-order necessary optimality conditions imply that locally optimal superposition operators share various characteristic properties with commonly used activation functions: They are always sigmoidal, continuously differentiable away from the origin, and typically possess a distinct kink at zero.

Further Informations
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations

Host
WIAS Berlin
Wednesday, 15.03.2023, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Christof Külske, Ruhr-Universität Bochum:
New states with non-singleton localization sets for gradient models on trees
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
Abstract: We consider gradient models on regular trees. These are integer-valued spin-models, where the spins (height variables) interact via a height-shift-invariant interaction between nearest neighbors on the tree. We construct spatially homogeneous infinite-volume states, which localize on finite subsets of the local state space. This holds under suitable low-temperature assumptions. These states are new, as they are not convex combinations of the previously known homogeneous states with singleton concentration set. We also discuss related existence results for delocalized states. Joint work with: Alberto Abbondando, Florian Henning, Pietro Majer (arXiv: 2302.05398)

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Tuesday, 14.03.2023, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Emilio Ferrucci, University of Oxford:
Branched Itô formula and Itô-Stratonovich correction (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Thursday, 09.03.2023, 14:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Thomas O'Leary Roseberry, University of Texas, USA:
Enabling efficient UQ and optimization with derivative-informed neural operators (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
Outer-loop problems arising in scientific applications such as Bayesian uncertainty quantification, and further optimization under uncertainty, require repeated evaluation of computationally intensive numerical models for varying parameters, making their solution intractable when one is constrained to use a high-fidelity model. Neural operators offer a means of explicitly learning maps from model parameters to outputs, thus enabling efficient solution of these outer loop problems. However, an essential ingredient for the scalable solution of high-dimensional is parametric derivative information, which can have the effect of reducing the dimensionality of the problem, and improving algorithmic convergence.In this talk we will present efficient strategies for learning high-dimensional derivative information via neural operators. By exploiting compactness of high-dimensional maps, if it exists, one can both generate and learn high dimensional derivative information where the dominant computational costs can be made independent of the discretization dimensions. Numerical results demonstrate that this additional derivative information improves the accuracy of the function approximation, and additionally is necessary to produce neural operators with reliable approximations of high-dimensional parametric derivatives. Numerical examples will demonstrate how these derivative informed neural operators can be used to accelerate the solutions of stochastic optimization problems and high-dimensional inference problems.This work is a collaboration with Omar Ghattas, Dingcheng Luo, Peng Chen and Umberto Villa.

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/95642353605?pwd=RXRhZWVHWjc0K0dkU3FJV0p5RGdOUT09 Meeting-ID: 956 4235 3605 Kenncode: 278202

Host
WIAS Berlin
Wednesday, 01.03.2023, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Partha Pratim Ghosh, TU Braunschweig:
A Last Progeny Modified Branching Random Walk
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
In this work, we consider a modification of the usual Branching Random Walk (BRW), where we give certain independent and identically distributed (i.i.d.) displacements to all the particles at the n-th generation, which may be different from the driving increment distribution. We call this process a last progeny modified branching random walk (LPM-BRW). Depending on the value of a parameter, θ, we classify the model in three distinct cases, namely, the boundary case, below the boundary case, and above the boundary case. Under very minimal assumptions on the underlying point process of the increments, we show that at the boundary case, when θ takes a particular value θ_0, the maximum displacement converges to a limit after only an appropriate centering, which is of the form c_1n - c_2log(n). We give an explicit formula for the constants c_1 and c_2 and show that c_1 is exactly the same, while c_2 is 1/3 of the corresponding constants of the usual BRW. We also characterize the limiting distribution. We further show that below the boundary (that is, when θ < θ_0), the logarithmic correction term is absent. For above the boundary case (that is, when θ > θ_0), we have only a partial result, which indicates a possible existence of the logarithmic correction in the centering with exactly the same constant as that of the classical BRW. For θ ≤ θ_0, we further derive Brunet- Derrida-type results of point process convergence of our LPM-BRW to a decorated Poisson point process. Similar results have been obtained also for the time inhomogeneous setting. Surprisingly, the limits in this case depend only on the increments in the initial fraction of time. Under very minimal assumptions, we also derive the large deviation principle (LDP) for the right-most position of a particle in generation n. As a byproduct, we also complete the LDP for the classical model, which complements the earlier work by Gantert and Höfelsauer. Our proofs are based on a novel method of coupling the maximum displacement with a linear statistic associated with a more well-studied process in statistics, known as the smoothing transformation.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Friday, 24.02.2023, 13:00 (WIAS-Library)
E-Coffee-Lecture
Dr. Jürgen Fuhrmann, WIAS:
The software development strategy of WIAS. We want to hear your feedback
more ... Location
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411

Host
WIAS Berlin
Thursday, 23.02.2023, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Élie de Panafieu, Nokia Bell Labs, Frankreich:
Active clustering of a set using pairwise comparisons
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
We analyze algorithms that reconstruct a set partition using pairwise comparisons, asking an oracle whether two elements belong to the same block. The goal is to minimize the average number of queries to the oracle. This problem is reminiscent of sorting: instead of a permutation, a set partition is recovered. In the case where the set partition is drawn uniformly at random, we characterize the optimal algorithms, prove they share the same distribution on the number of queries and analyze this distribution. We also investigate a random set partition model where each element chooses its block independently following a fixed distribution. This work is motivated by the annotation of training data for supervised learning. Published at Neurips with Quentin Lutz (Nokia Bell Labs), Maya Stein (University of Chile) et Alex Scott (Oxford University).

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Wednesday, 22.02.2023, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. A.F.M. ter Elst, University of Auckland, Neuseeland:
Kato's inequality and degenerate elliptic operators (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We consider a second-order divergence form operator with real bounded coefficients and maximal domain in L_p(R^d). We assume that the matrix of principal coefficients is positive semi-definite. Under suitable differentiability conditions on the coefficients we show that the operator is the (minus) generator of a C_0-semigroup if p is finite, and if in addition p > 1, then the space of test-functions is a core for the maximal operator. We also discuss perturbation of the maximal operator with a positive potential and optimal results in one dimension, that is if d=1. This talk is based on joint work with Wolfgang Arendt and with Tan Do.

Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 21.02.2023, 13:30 (WIAS-405-406)
Seminar Materialmodellierung
Prof. Alberto Salvadori, Università degli Studi di Brescia, Italien:
Modeling and simulations towards the design of high performance batteries
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Host
WIAS Berlin
Thursday, 16.02.2023, 14:00 (Online Event)
Seminar Nonsmooth Variational Problems and Operator Equations
Dr. Christian Parkinson, University of Arizona, USA:
The Hamilton--Jacobi formulation of optimal path planning for autonomous vehicles (online talk)
more ... Location
Online Event

Abstract
We present a partial-differential-equation-based optimal path planning framework for simple self-driving cars. This formulation relies on optimal control theory, dynamic programming, and a Hamilton-Jacobi-Bellman equation, and thus provides an interpretable alternative to black-box machine learning algorithms. We design grid-based numerical methods used to resolve the solution to the Hamilton-Jacobi-Bellman equation and generate optimal trajectories. We then describe how efficient and scalable algorithms for solutions of high dimensional Hamilton-Jacobi equations can be used to solve similar problems in higher dimensions and in nearly real-time. We demonstrate all of our methods with several examples.

Further Informations
Seminar Nichtglatte Variationsprobleme und Operatorgleichungen

Host
WIAS Berlin
Wednesday, 15.02.2023, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Claude Le Bris, École des Ponts ParisTech & INRIA, Frankreich:
Defects in homogenization theory and related computational issues (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We review a series of works that address homogenization for partial differential equations with highly oscillatory coefficients. A prototypical setting is that of periodic coefficients that are locally, or more globally perturbed. We investigate the homogenization limits obtained, first for linear elliptic equations, both in conservative and non conservative forms, and next for nonlinear equations such as Hamilton--Jacobi type equations. Some emphasis will also be placed on the consequences of the above theoretical endeavour on strategies for modeling actual materials and simulating them using multiscale approaches, such as MsFEM methods. The works presented have been completed in collaboration with a number of colleagues, in particular with Y. Achdou, X. Blanc, P. Cardaliaguet, F. Legoll, P.-L. Lions, A. Lozinski, and R. Biezemans, R. Goudey.

Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 15.02.2023, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Jovanka Lili Matic, Humboldt-Universität zu Berlin:
Global sensitivity analysis in the presence of missing values (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We investigate global variable importance in the presence of missing values. We assume that missing values are present in the random input vector. In this context, we analyse the dependence structure in the input vector under three missingness mechanisms: Missing Completely at Random (MCAR), Missing at Random (MAR), and Missing Not a Random (MNAR) (Rubin and Mealli, 2015). In case of global independence, we define the Hoeffding-Sobol/Functional ANOVA decomposition and Sobol indices in the presence of missing values. We also show that no dependent input vector satisfies the requirements for the Stone-Hooker dependent variable ANOVA. First Order Sobol indices of observed variables provide bounds for Shapley effects in the presence of missing values. Lastly, we analyze the consequences of two common missing value management techniques: Complete-case analysis (CC) and Imputation. The study is concluded with a numerical simulation.

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Tuesday, 14.02.2023, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Prof. Dr. Tim Laux, Universität Bonn:
The large-data limit of the MBO scheme for data clustering (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
The MBO scheme is an efficient algorithm for data clustering, the task of partitioning a given dataset into several meaningful clusters. In this talk, I will present the first rigorous analysis of this scheme in the large-data limit. The starting point for the first part of the talk is that each iteration of the MBO scheme corresponds to one step of implicit gradient descent for the thresholding energy on the similarity graph of the dataset. It is then natural to think that outcomes of the MBO scheme are (local) minimizers of this energy. We prove that the algorithm is consistent, in the sense that these (local) minimizers converge to (local) minimizers of a suitably weighted optimal partition problem. To study the dynamics of the scheme, we use the theory of viscosity solutions. The main ingredients are (i) a new abstract convergence result based on quantitative estimates for heat operators and (ii) the derivation of these estimates in the setting of random geometric graphs. To implement the scheme in practice, two important parameters are the number of eigenvalues for computing the heat operator and the step size of the scheme. Our results give a theoretical justification for the choice of these parameters in relation to sample size and interaction width. This is joint work with Jona Lelmi (U Bonn).

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Monday, 13.02.2023, 10:30 (WIAS-405-406)
Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Dr.-Ing. Julia Kowal, Technische Universität Berlin:
Working principle and ageing of batteries
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Host
WIAS Berlin
Wednesday, 08.02.2023, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Jun. Prof. Dr. Patrick Tolksdorf, Johannes Gutenberg-Universität Mainz:
Lp-extrapolation of the generalized Stokes operator (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Please see here.

Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 08.02.2023, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Dave Jacobi, TU Berlin:
Super-Brownian motion with dormancy
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
The majority of species exhibit a behaviour called Dormancy, in which the individuals switch into a state of low metabolic activity, that protects them from harsh environmental conditions and in this way increases their chance of survival. Therefore models from mathematical population biology have to incorporate this phenomenon. We will extend the classical Super-Brownian motion, which is a measure-valued branching Markov process, to model Dormancy and retrieve a process that we will call on/off Super-Brownian motion. This process has many interesting properties that are often closely related to classical Super-Brownian motion, but at the same time exhibit new and different behaviour. We will go on a round trip of these properties. Also, if time permits, we will look at the close relation between the total mass process of superprocesses and an excursion process, which can help us understand the genealogy of these measure-valued processes.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Wednesday, 08.02.2023, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. Dr. Vanessa Didelez, Universität Bremen:
Causal reasoning and causal discovery with applications in epidemiology
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Many data analyses ultimately aim at answering causal research questions: We may want to assess and quantify the potential effects of certain decisions, interventions or policies, e.g. will a sugar tax or more playgrounds reduce childhood obesity? Will participation in a special training programme for the unemployed increase the chances of finding employment? Is a national mammography screening programme actually helpful in preventing deaths from breast cancer? Such questions are about causal relations and go beyond mere prediction; indeed, methods that are optimised for prediction will often give biased results for causal targets. Especially when we use non-experimental, i.e. observational data to try and answer questions about causal relations, tailored methods relying on specific assumptions are called for. The talk will review the main concepts, fundamental assumptions and basic principles for causal learning and focus on methods of causal discovery (aka structure learning). The latter have their roots in probabilistic approaches to artificial intelligence (AI) and, together with broader methods of causal inference in general, have recently seen a great revival in AI. This increased activity might be due to the realization "that many hard open problems of machine learning and AI are intrinsically related to causality" (Schölkopf, 2019). However, applications in epidemiology still pose a number of practical challenges; these include, for instance, handling incomplete, mixed, heterogenous and temporal data. I will illustrate some of the methods, their issues and proposed solutions with the analysis of a children's cohort data.

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Tuesday, 07.02.2023, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
PhD Alain Rossier, University of Oxford, GB:
Asymptotic analysis of deep residual networks (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation (SDE) or neither of these. Furthermore, we are able to formally prove the linear convergence of gradient descent to a global optimum for the training of deep residual networks with constant layer width and smooth activation function. We further prove that if the trained weights, as a function of the layer index, admit a scaling limit as the depth increases, then the limit has finite 2-variation.

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Wednesday, 01.02.2023, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Assoc. Prof. Dr. Tamara Fastovska, Karazin Kharkiv National University, Ukraine:
Asymptotic behaviour of solutions to transmission problems for elastic beams (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In this talk, we consider transmission problems describing dynamics of elastic beams consisting of two parts with dierent elastic properties. In particular, we investigate the full von Karman model and the Bresse model for arch beams. We prove the properties sucient for existence of global attractors, namely, the gradient structure and asymptotic smoothness. For the Bresse model we also investigate limiting situations as the curvature of the beam tends to zero both for finite time intervals and in the sense of upper-simicontinuity of attractors.

Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 01.02.2023, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Alice Callegaro, TU München/JGU Mainz:
Survival and complete convergence for a branching annihilating random walk
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
Branching systems with competition are interacting particle systems which have gained popularity as models for the reproduction of a spatial population with limited environmental resources. We study a branching annihilating random walk (BARW) in which particles move on the lattice and evolve in discrete generations. Each particle produces a Poissonian number of offspring which independently move to a uniformly chosen site within a fixed distance from their parent's position. Whenever a site is occupied by at least two particles, all the particles at that site are annihilated. This feature means that the system is not monotone and therefore the usual comparison methods are not applicable. We show that the system survives via coupling arguments and comparison with oriented percolation, making use of carefully defined density profiles which expand in time and are reminiscent of discrete travelling wave solutions. In the second part of the talk I will explain how a refinement of this technique can be employed to show complete convergence for the BARW in certain parameter regimes. The talk in based on a joint work with Matthias Birkner (JGU Mainz), Jiří Černý (University of Basel), Nina Gantert (TU Munich) and Pascal Oswald (University of Basel/JGU Mainz).

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Wednesday, 01.02.2023, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. Radu Stoica, Université de Lorraine , Frankreich:
Random structures and patterns in spatio-temporal data: probabilistic modelling and statistical inference (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
The useful information carried by spatio-temporal data is often outlined by geometric structures and patterns. Filaments or clusters induced by galaxy positions in our Universe are such an example. Two situations are to be considered. First, the pattern of interest is hidden in the data set, hence the pattern should be detected. Second, the structure to be studied is observed, so relevant characterization of it should be done. This talk is structured in four parts. The first part presents the construction of different marked point processes together with their properties, such that characteristics of the patterns of interested are modelled by these processes. Second, tailored to the model MCMC dynamics to simulate the previous models are presented. A discussion related to the performances of these algorithms and comparison with exact simulation methods are provided. Third, on this basis, inference procedures are derived. They include level sets estimators, global optimisation, Approximate Bayesian Computation. Finally, applications on cosmological and geological real data are shown.

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Tuesday, 31.01.2023, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Matthias Liero, WIAS Berlin:
On the geometry of the Hellinger-Kantorovich space (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Friday, 27.01.2023, 13:00 (WIAS-Library)
E-Coffee-Lecture
Dr Karsten Tabelow, WIAS:
On criticality: orcas, sex, and the pandemic
more ... Location
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411

Host
WIAS Berlin
Thursday, 26.01.2023, 10:15 (WIAS-406)
Seminar Nichtlineare Optimierung und Inverse Probleme
Dr. Igor Voulis, Georg-August-Universität Göttingen:
Optimality of adaptive stochastic Galerkin methods for affine-parametric elliptic PDEs
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Host
WIAS Berlin
Wednesday, 25.01.2023, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Alexander Drewitz, Universität zu Köln:
Percolation, long-range correlations and critical exponents on transient graphs
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
Percolation models have been playing a fundamental role in statistical physics for several decades by now. They had initially been investigated in the gelation of polymers during the 1940s by chemistry Nobel laureate Flory and Stockmayer. From a mathematical point of view, the birth of percolation theory was the introduction of Bernoulli percolation by Broadbent and Hammersley in 1957, motivated by research on gas masks for coal miners. One of the key features of this model is the inherent stochastic independence which simplifies its investigation, and which has led to deep mathematical results. During recent years, the investigation of the more realistic and at the same time more complex situation of percolation models with long-range correlations has attracted significant attention. We will exhibit some recent progress for the Gaussian free field with a particular focus on the understanding of the critical parameters in the associated percolation models. What is more, we also survey recent progress in the understanding of the model at criticality via its critical exponents as well as the universality in the local geometry of the underlying graph. This talk is based on joint works with A. Prévost (U Geneva) and P.-F. Rodriguez (Imperial College).

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Wednesday, 25.01.2023, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Dr. Maria Grith, Erasmus University Rotterdam, Niederlande:
The block-autoregressive model in non-standard bases (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We propose a new modeling approach for univariate time series with component dynamics that correspond to different aggregation schemes. The model is called the block-autoregressive (BAR) model, as it is based on the application of a vector autoregressive model to univariate data that is partitioned into 'blocks' of observations. These blocks of observations are transformed into linear combinations by an orthonormal basis change, which can unveil linear dynamics that can otherwise be obfuscated in the time-space. Model selection and estimation are intertwined and involve a sequential regression and testing procedure. We assess the goodness of fit of the estimated model with a parametric bootstrap and asymptotic chi-squared test. We rely upon a relationship between the covariance of the innovations in the time and transformed space, to identify and estimate the latent orthonormal basis of a process. We discuss several simulated and empirical examples which demonstrate both the flexibility and the explanatory potential of the BAR model.

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Tuesday, 24.01.2023, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Oleg Butkovsky, WIAS Berlin:
Stochastic equations with singular drift driven by fractional Brownian motion (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Thursday, 19.01.2023, 14:00 (WIAS-ESH)
Seminar Numerische Mathematik
Michele Pütz, Brandenburgische Technische Universität:
Quadrature-based moment methods for the solution of population balance equations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Particulate systems of many kinds are mathematically described by a multivariate number density function (NDF) whose evolution is governed by a so-called population balance equation (PBE). Typically, such equations are characterized by a high dimensionality and, accordingly, high computational costs for the numerical solution. Quadrature-based moment methods (QBMMs) aim to efficiently approximate solutions to PBEs by solving only for a set of moments instead of the NDF and closing the PBE using Gaussian quadrature rules. The upcoming presentation will give an introduction to QBMMs, elaborate on limitations and challenges associated with non-smooth terms in the moment equations using physical examples and provide some results related to the performance and accuracy of QBMMs. The talk will be conducted hybrid. Zoom coordinates are sent around in time.

Further Informations
Seminar Numerische Mathematik

Host
WIAS Berlin
Wednesday, 18.01.2023, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Florian Oschmann, Czech Academy of Sciences, Tschechische Republik:
Stratified fluids: On pancakes and non-local temperatures (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We investigate the rigorous derivation of two models for incompressible fluid flow: a) Majda's “stack of pancakes” model, governing essentially two-dimensional flow with momentum coupling in the vertical variable; b) the Oberbeck--Boussinesq approximation, governing the motion of a heat conducting fluid heated from below and cooled from above. Their derivation from the full compressible Navier--Stokes--Fourier system has been done for a) the inviscid (Euler) case where no coupling occurs, and b) the case of Neumann BC for the temperature. We will investigate the rigorous justification of both models for the case of viscous fluids with temperature Dirichlet BC, and show that a) indeed there is vertical coupling, and b) an unexpected temperature term arises. This is joint work with Peter Bella (TU Dortmund) and Eduard Feireisl (CAS).

Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 18.01.2023, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Dr. Tim Jahn, Universität Bonn:
Discretisation-adaptive regularisation of statistical inverse problems (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We consider linear inverse problems under white (non-Gaussian) noise. We introduce a discretisation scheme to apply the discrepancy principle and the heuristic discrepancy principle, which require bounded data norm. Choosing the discretisation dimension in an adaptive fashion yields convergence, without further restrictions for the operator, the distribution of the white noise or the unknown ground solution. We discuss connections to Lepski's method and apply the technique to ill-posed integral equations with noisy point evaluations. We show that here discretisation-adaptive regularisation can be used in order to reduce the numerical complexity.

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Monday, 16.01.2023, 14:00 (WIAS-406)
Seminar Numerische Mathematik
Dr. Michael F. Herbst, RWTH Aachen:
Black-box algorithms and robust error control for density-functional theory
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
Today's ubiquitous data-driven workflows allow scientists to expand the limits of length and time scales in materials simulations. In this setting questions related to the robustness and accuracy of simulation protocols as well as the reproducibility of obtained simulation data are more pressing then ever. Due to the complexity of underlying physical models (non-linear PDEs, multi-linear algebra) tackling these issues is inherently an interdisciplinary endeavour. However, close collaboration of application scientists with researchers from mathematics or computer science requires software, which can support research thrusts all the way from model problems to full-scale applications. With the aim to overcome this obstacle we started the density-functional toolkit (DFTK, https://dftk.org) about four years ago. DFTK is a Julia package for Kohn-Sham density-functional theory (DFT), which is highly accessible (only 7000 of code). Based on Julia's composable software ecosystem it integrates with standard HPC libraries (MPI, CUDA) and supports algorithmic differentiation. This has already enabled cross-disciplinary advances on error estimation or the developments of more robust algorithms. Of those I will highlight two recent efforts. Firstly our work on the DFT ground state problem involving better preconditioners for the underlying fixed-point equations and secondly the development of more efficient algorithms for response calculations. The latter are the key equations for computing many relevant materials properties and represent a central building block in our efforts to make DFTK fully algorithmically differentiable. In the final part of my talk I will sketch the current state of our work along this direction and present some application examples.

Host
WIAS Berlin
Humboldt-Universität zu Berlin
Wednesday, 11.01.2023, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Ass. Prof. Dr. Oliver Tse, Eindhoven University of Technology, Niederlande:
Scharfetter--Gummel for aggregation-diffusion equations: Gradient structures and their limits (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In this talk, I will present some new insights into the variational structure of the Scharfetter--Gummel scheme for aggregation-diffusion equations. In particular, we propose a gradient structure that allows one to prove asymptotic limits in two regimes - the continuum limit and the zero-diffusion limit. This is a work in progress with Anastasiia Hraivoronska and André Schlichting.

Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 11.01.2023, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Chiranjib Mukherjee, WWU Münster:
Homogenization of Hamilton--Jacobi--Bellman equations on continuum percolation clusters
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
We prove homogenization of Hamilton-Jacobi-Bellman (HJB) equations on continuum percolation clusters, almost surely w.r.t. the law of the environment when the origin belongs to the unbounded component in the continuum. Here, the viscosity term carries a degenerate matrix, the Hamiltonian is convex and coercive w.r.t. the degenerate matrix and the underlying environment is non-elliptic and its law is non-stationary w.r.t. the translation group. We do not assume uniform ellipticity inside the percolation cluster, nor any finite-range dependence (i.i.d.) on the environment. In this setup, we develop an approach based on the coercivity property of the Hamiltonian as well as a relative entropy structure (both being intrinsic properties of HJB) and make use of the random geometry of continuum percolation. Joint work with Rodrigo Bazaes (Münster) and Alexander Mielke (Berlin).

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Tuesday, 10.01.2023, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Robert Gruhlke, WIAS Berlin:
Wasserstein polynomial chaos and Langevin dynamics (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
An unsupervised learning approach for the computation of an explicit functional representation of a random vector is presented, which only relies on a finite set of samples from an unknown distribution. Motivated by recent advances with computational optimal transport for estimating Wasserstein distances, we develop a generative model denoted as Wasserstein multi-element polynomial chaos expansion (WPCE). It relies on the minimization of a regularized empirical Wasserstein metric known as debiased Sinkhorn divergence. Since the used PCE grows exponentially in the number of underlying input random coordinates, we introduce an appropriate low-rank format given as stacks of tensor trains. This alleviates the curse of dimensionality, leading to only linear dependence on the input dimension. Ensemble methods nowadays are ubiquitous for the solution of Bayesian inference problems. We discuss recent advances based on state-of-the-art samplers such as Affine Invariant Langevin Dynamics (ALDI) that allow for increased convergence speed and in turn reduce the required number of forward calls encoded in the drift term of the underlying stochastic differential equation. This improvement is realised through possible adaptive ensemble enrichment and an adapted Langevin dynamics based on a homotopy formalism. Optionally, the history of particles obtained within the solution process of the Langevin dynamics then can be used to numerically construct a push forward map in terms of WPCE. Once computed, this provides functional access to the posterior without the need of further forward model evaluations.

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Wednesday, 04.01.2023, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Franz Besold, Humboldt Universität zu Berlin:
Adaptive weights community detection (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Due to the technological progress of the last decades, Community Detection has become a major topic in machine learning. However, there is still a huge gap between practical and theoretical results, as theoretically optimal procedures often lack a feasible implementation and vice versa. This paper aims to close this gap and presents a novel algorithm that is both numerically and statistically efficient. Our procedure uses a test of homogeneity to compute adaptive weights describing local communities. The approach was inspired by the Adaptive Weights Community Detection (AWCD) algorithm by Adamyan et al. (2019). This algorithm delivered some promising results on artificial and real-life data, but our theoretical analysis reveals its performance to be suboptimal on a stochastic block model. In particular, the involved estimators are biased and the procedure does not work for sparse graphs. We propose significant modifications, addressing both shortcomings and achieving a nearly optimal rate of strong consistency on the stochastic block model. Our theoretical results are illustrated and validated by numerical experiments.

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Friday, 16.12.2022, 13:00 (WIAS-Library)
E-Coffee-Lecture
Dr. Eleanor Eife-Horn, WIAS:
Introduction to the MyProTime absence management system and updates on the federal travel expenses act
more ... Location
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411

Further Informations
Online (hybrid) event

Host
WIAS Berlin
Wednesday, 14.12.2022, 10:30 (WIAS-Library)
Seminar in Machine Learning and Data-Driven Optimization
Heiner Kremer/Yassine Nammour, Max Planck Institute for Intelligent Systems:
Distributionally robust machine learning via conditional moment restrictions (hybrid talk)
more ... Location
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411

Further Informations
The talk is also given via Zoom: https://us02web.zoom.us/j/8994552597

Host
WIAS Berlin
Tuesday, 13.12.2022, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Amal Alphonse, WIAS Berlin:
Risk-averse optimal control of random elliptic variational inequalities (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
In this talk, I will discuss a risk-averse optimal control problem governed by an elliptic variational inequality (VI) subject to random inputs. I will derive two forms of first-order stationarity conditions for the problem by passing to the limit in a penalised and smoothed approximating control problem. The lack of regularity with respect to the uncertain parameters and complexities induced by the presence of the risk measure give rise to delicate analytical challenges seemingly unique to the stochastic setting. To finish, I will briefly discuss a path-following stochastic approximation algorithm and demonstrate it on an example.

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Tuesday, 13.12.2022, 13:30 (WIAS-ESH)
Seminar Numerische Mathematik
Xu Li, Shandong University, China, Volksrepublik:
Inf-sup stabilized Scott--Vogelius elements for incompressible flows
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
This talk is concerned about the finite element methods for incompressible flows such as Stokes problem and Navier-Stokes problem. When designing the schemes for incompressible flows, one should consider the continuity requirement, inf-sup stability and divergence constraint simultaneously, which is a challenging problem. Traditionally, most of the finite element methods do not satisfy the divergence constraint exactly. One exception is the Scott--Vogelius elements, i.e., P_k-P_k-1 pairs, which are stable on some special meshes such as barycentric refined meshes. Here we introduce a new class of finite elements which stabilizes the Scott--Vogelius elements by enriching the velocity space with some Raviart--Thomas functions on general mesh, while maintaining the divergence-free property. Starting with the Stokes equations, we show the inf-sup stability, the convergence analysis and the pressure-robustness property of the newly proposed element. Also a reduced version of the method, an equivalent P_k-P_0 discretization, is discussed. Finally we extend this element to the Navierß-Stokes problem, where the convection-robustness property and the discretization of the nonlinear term is also of interest and importance.

Host
WIAS Berlin
Wednesday, 07.12.2022, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Daniel Heydecker, MPI Leipzig:
From LDPs of the Kac Process to the H-Theorem
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
It is well-recognised that the large deviations of particle systems are connected to the appearance of a gradient flow formulation through a reformulation of the dynamical large deviations cost. In this talk, I will discuss a simple proof of Boltzmann's H-Theorem in the spatially homogeneous Boltzmann equation, which yields the equality between entropy and integrated entropy dissipation under quite general conditions. Time allowing, I will also discuss recent work applying the same principles to the porous medium equation.

Further Informations
Seminar Interacting Random Systems

Host
WIAS Berlin
Tuesday, 06.12.2022, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Alexandra Suvorikova, WIAS Berlin:
Anomaly detection in biometric authentication (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
In this work we suggest a novel framework to detect user behaviour anomalies based on transfer learning approach combined with optimal transport techniques.

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Monday, 05.12.2022, 10:30 (WIAS-406)
Seminar in Machine Learning and Data-Driven Optimization
Yucen Luo, Max Planck Institute for Intelligent Systems:
Spectral representation learning for conditional moment models (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
Many problems in causal inference and economics can be formulated in the framework of conditional moment models, which characterize the target function through a collection of conditional moment restrictions. For nonparametric conditional moment models, efficient estimation has always relied on preimposed conditions on various measures of ill-posedness of the hypothesis space, which are hard to validate when flexible models are used. In this work, we address this issue by proposing a procedure that automatically learns representations with controlled measures of ill-posedness. Our method approximates a linear representation defined by the spectral decomposition of a conditional expectation operator, which can be used for kernelized estimators and is known to facilitate minimax optimal estimation in certain settings. We show this representation can be efficiently estimated from data, and establish $L_2$ consistency for the resulting estimator. We evaluate the proposed method on proximal causal inference tasks, exhibiting promising performance on high-dimensional, semi-synthetic data.

Further Informations
The talk is also given via Zoom: https://us02web.zoom.us/j/8994552597

Host
WIAS Berlin
Wednesday, 30.11.2022, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Tomáš Roubíček, Czech Academy of Sciences, Tschechische Republik:
Magnetism in the planet Earth and its mathematical modelling (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Two main mechanisms by which the planetary magnetism is manifested, i.e. magnetodynamo and paleomagnetism, will be presented, together with their mathematical models based on continuum thermomechanics at large deformations. The latter mechanism (paleomagnetism) will be restricted on thermoremanent magnetization where the antiferro-to-ferri-magnetic (or parra-to-ferro-magnetic) transition combined with solidification-melting are interesting phenomenona to be modelled.

Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 30.11.2022, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Julian Kern, WIAS Berlin:
A Fleming-Viot model with varying population size
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
One drawback of the popular Fleming--Viot model in population genetics is the assumed constant population size (in time and space). We consider a variant of this model that includes variations in the size of the total population intrinsically via heavy-tailed offspring distributions and compare it to the classical model. In particular, we obtain an analogous to the Wright--Fisher diffusion in the setting of large offsprings and discuss in what way it may be viewed as an extension of it.

Further Informations
Seminar Interacting Random Systems

Host
WIAS Berlin
Wednesday, 30.11.2022, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
PhD Mikołaj Kasprzak, University of Luxembourg:
How good is your Laplace approximation? Finite-sample error bounds for a variety of useful divergences (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
The Laplace approximation is a popular method of approximating an intractable Bayesian posterior by a suitably chosen Gaussian distribution. But can we trust this approximation for practical use? Its theoretical justification comes from the celebrated Bernstein-von Mises theorem (also known as the Bayesian CLT or BCLT). However, an obstacle to its wider use is the lack of widely applicable post-hoc checks on its quality. Our work provides closed-form, finite-sample quality bounds for the Laplace approximation that simultaneously(1) do not require knowing the true parameter, (2) control posterior means and variances, and (3) apply generally to models that satisfy the conditions of the asymptotic BCLT. In fact, our bounds work even in the presence of misspecification. We compute exact constants in our bounds for a variety of standard models, including logistic regression, and numerically demonstrate their utility. And we provide a framework for analysis of more complex models. This is joint work with Ryan Giordano (MIT) and Tamara Broderick (MIT). A preliminary version of the work is available here: https://arxiv.org/abs/2209.14992.

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Tuesday, 29.11.2022, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Thomas Wagenhofer, Technische Universität Berlin:
Reconstructing volatility: Pricing of index options under rough volatility (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
In [ABOBF02, ABOBF03] Avellaneda et al. pioneered the pricing and hedging of index options - products highly sensitive to implied volatility and correlation assumptions - with large deviations methods, assuming local volatility dynamics for all components of the index. We here present an extension applicable to non-Markovian dynamics and in particular the case of rough volatility dynamics.

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Friday, 25.11.2022, 13:00 (WIAS-Library)
E-Coffee-Lecture
Dr. Renita Danabalan, WIAS:
From Interviewee to Interviewer: Perspectives of both sides
more ... Location
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411

Host
WIAS Berlin
Wednesday, 23.11.2022, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Richard Schubert, Universität Bonn:
A variational approach to data-driven problems in fluid mechanics (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In this talk, we discuss a data-driven approach to viscous fluid mechanics. Typically, in order to describe the behaviour of fluids, two different kinds of modelling assumptions are used. On the one hand, there are first principles like the balance of forces or the incompressibility condition. On the other hand there are material specific constitutive laws that describe the relation between the strain and the viscous stress of the fluid. Combining both, one obtains the partial differential equations of fluid mechanics like the Stokes or Navier--Stokes equations. The constitutive laws are obtained by fitting a law from a certain class (for example linear, power law, etc.) to experimental data. This leads to modelling errors. Instead of using a constitutive relation, we introduce a data-driven formulation that has previously been examined in the context of solid mechanics and directly draws on material data. This leads to a variational solution concept, that incorporates differential constraints coming from first principles and produces fields that are optimal in terms of closeness to the data. In order to derive this formulation we recast the differential constraints of fluid mechanics in the language of constant-rank differential operators. We will see that the data-driven solutions are consistent with PDE solutions if the data are given by a constitutive law. Furthermore we show a Gamma-convergence result for the functionals arising in the data-driven fluid mechanical problem which implies that the method is well-adapted to the convergence of experimental data through increasing experimental accuracy. This is based on joint work with Christina Lienstromberg (Stuttgart) and Stefan Schiffer (Leipzig).

Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 23.11.2022, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Alexei Kroshnin, WIAS Berlin:
Robust k-means clustering in Hilbert and metric spaces (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In this talk, we consider the robust algorithms for the k-means clustering (quantization) problem where a quantizer is constructed based on N independent observations. While the well-known asymptotic result by Pollard shows that the existence of two moments is sufficient for strong consistency of an empirically optimal quantizer in Rd, non-asymptotic bounds are usually obtained under the assumption of bounded support. We discuss a robust k-means in Hilbert and metric spaces based on trimming, and prove non-asymptotic bounds on the excess distortion, which depend on the probability mass of the lightest cluster and the second moment of the distribution.

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Tuesday, 22.11.2022, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Pavel Dvurechensky, WIAS Berlin:
Generalized self-concordant analysis of Frank-Wolfe algorithms (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
We propose several variants of the Frank-Wolfe method for minimizing generalized self-concordant (GSC) functions over compact sets. Such problems are ill-conditioned and are motivated by machine learning applications such as inverse covariance estimation or distance-weighted discrimination problems in support vector machines. We obtain O(1/k) convergence rate guarantees in the general situation and linear convergence under strong convexity and additional assumptions.

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Thursday, 17.11.2022, 09:30 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Tim Böhnlein, Technische Universität Darmstadt:
On necessary and sucient conditions for Gaussian estimates of elliptic operators subject to mixed boundary conditions (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Given an open subset in the Euclidean space, we consider divergence form operators with bounded, measurable and complex coefficients subject to mixed boundary conditions. We find equivalent conditions under which the kernel of the semigroup generated by the divergence form operator is Höolder continuous and satisfies pointwise Gaussian upper bounds. The geometric assumptions reach far beyond the Lipschitz class and we do not impose any condition on the interface between Dirichlet and Neumann part.

Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 16.11.2022, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Moritz Egert, Technische Universität Darmstadt:
Four critical numbers for elliptic systems with block structure (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 16.11.2022, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Jonas Köppl, WIAS Berlin:
Dynamical Gibbs variational principles for irreversible interacting particle systems with applications to attractor properties
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
We consider irreversible translation-invariant interacting particle systems on the d-dimensional hypercubic lattice with finite local state space, which admit at least one Gibbs measure as a time-stationary measure. Under some mild degeneracy conditions on the rates and the specification, we prove that the relative entropy is non-increasing as a function of time and that a vanishing relative entropy loss for a translation-invariant measure implies that the measure is Gibbs w.r.t. the same specification as the time-stationary Gibbs measure. As an application, we obtain the attractor property for irreversible interacting particle systems, which says that any weak limit point of any trajectory of translation-invariant measures is a Gibbs measure w.r.t. the same specification as the time-stationary measure. This extends previously known results to fairly general irreversible interacting particle systems.

Further Informations
Seminar Interacting Random Systems

Host
WIAS Berlin
Wednesday, 16.11.2022, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. Aila Särkkä, Chalmers University of Technology and University of Gothenburg , Schweden:
Anisotropy analysis and modelling of spatial point patterns (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In the early spatial point process literature, observed point patterns were typically small and no repetitions were available. It was natural to assume that the patterns were realizations of stationary and isotropic point processes. Nowadays, large data sets with repetitions have become more and more common and it is important to think about the validity of these assumptions. Non-stationarity has received quite a lot of attention during the recent years and it is straightforward to include it in many point process models. Isotropy, on the other hand, is often still assumed without further checking, and even though there are several tools suggested to detect isotropy and test for it, they have not been so widely used. This talk will give an overview of nonparametric methods for anisotropy analysis of (stationary) point processes ([3], [4], [5]). Methods based on nearest neighbour and second order summary statistics as well as on spectral and wavelet analysis will be discussed. The techniques will be illustrated on both a clustered and a regular example. In the second part of the talk, one of the methods will be used to estimate the deformation history in polar ice using the measured anisotropy of air inclusions from deep ice cores [2]. In addition, an anisotropic point process model for nerve fiber data will be presented [1]. References: [1] Konstantinou K and Särkkä A (2022). Pairwise interaction Markov model for 3D epidermal nerve fiber endings. To appear in Journal of Microscopy. [2] Rajala T, Särkkä A, Redenbach C, and Sormani M (2016). Estimating geometric anisotropy in spatial point patterns. Spatial Statistics 15, 100?114. [3] Rajala T, Redenbach C, Särkkä A, and Sormani M (2018). A review on anisotropy analysis of spatial point patterns. Spatial Statistics 28, 141?168. [4] Rajala T, Redenbach C, Särkkä,A, and Sormani M (2022). Tests for isotropy in spatial point patterns. Under revision. [5] Sormani M, Redenbach C, Särkkä A and Rajala T (2020). Second order directional analysis of point processes revisited. Spatial Statistics 38, 100456.

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Thursday, 10.11.2022, 11:00 (WIAS-Library)
Seminar Nonsmooth Variational Problems and Operator Equations
Dr. Jonas Latz, Heriot-Watt University:
Analysis of stochastic gradient descent in continuous time
more ... Location
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411

Further Informations
Seminar Nichtglatte Variationsprobleme und Operatorgleichungen

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 09.11.2022, 10:00 (WIAS-HVP-3.13)
Forschungsseminar Mathematische Statistik
Prof. Claudia Schillings, Freie Universität Berlin:
The convergence of the Laplace approximation and noise-level-robust computational methods for Bayesian inverse problems (hybrid talk)
more ... Location
Weierstraß-Institut, Hausvogteiplatz 11A, 10117 Berlin, 3. Etage, Raum: 3.13

Abstract
The Bayesian approach to inverse problems provides a rigorous framework for the incorporation and quantification of uncertainties in measurements, parameters and models. We are interested in designing numerical methods which are robust w.r.t. the size of the observational noise, i.e., methods which behave well in case of concentrated posterior measures. The concentration of the posterior is a highly desirable situation in practice, since it relates to informative or large data. However, it can pose a computational challenge for numerical methods based on the prior measure. We propose to use the Laplace approximation of the posterior as the reference measure for the numerical integration and analyze the efficiency of Monte Carlo methods based on it.

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
November 9 – 11, 2022 (WIAS-ESH)
Workshop/Konferenz: MaRDI Annual Workshop 2022 (Hybrid Event)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
The MaRDI annual workshop, a hybrid event, is a chance for all of us who are working in MaRDI and those who are interested in MaRDI-related topics to meet, exchange ideas and get caught up on the latest happenings within the initiative.

Host
WIAS Berlin
Tuesday, 08.11.2022, 13:30 (WIAS-ESH)
Seminar Materialmodellierung
Prof. Dr. Leonid Berlyand, Pennsylvania State University:
Asymptotic stability in a free boundary PDE model of active matter (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We begin with a brief overview of the rapidly developing research area of active matter (a.k.a. active materials). These materials are intrinsically out of thermal equilibrium resulting in novel physical properties whose modeling requires development of new mathematical tools. We next focus on study the onset of motion of a living cell (e.g., a keratocyte) driven by myosin contraction with focus on a transition from unstable radial stationary states to stable asymmetric moving states. We introduce a two-dimensional free-boundary PDE model that generalizes a previous one-dimensional model by combining a Keller--Segel model, Hele--Shaw kinematic boundary condition, and the Young--Laplace law with a novel nonlocal regularizing term. This nonlocal term precludes blowup or collapse by ensuring that membrane-cortex interaction is sufficiently strong. We found a family of asymmetric traveling solutions bifurcating from stationary solutions. Our main result is the nonlinear asymptotic stability of traveling wave solutions that model observable steady cell motion. We derived and rigorously justified an explicit asymptotic formula for the stability determining eigenvalue via asymptotic expansions in a small speed of cell. This formula greatly simplifies the computation of this eigenvalue and shows that stability is determined by the change in total myosin mass when stationary solutions bifurcate to traveling solutions. Our spectral analysis reveals the physical mechanisms of stability. It also leads to interesting mathematics due to non-selfadjointness of the linearized problem which is a signature of active matter out-of-equilibrium systems. If time permits, we will discuss work in progress on fingering instability in multicellular tissue spreading. This is joint work with V. Rybalko and C. Safsten published in Transactions of AMS (to appear) and Phys. Rev.B, 2022.

Host
WIAS Berlin
Wednesday, 02.11.2022, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Alexander Mielke, WIAS Berlin:
On time-splitting methods for gradient flows with two dissipation mechanisms (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 02.11.2022, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. Dr. Johannes Schmidt-Hieber, University of Twente , Niederlande:
Overparametrization and the bias-variance dilemma (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
For several machine learning methods such as neural networks, good generalisation performance has been reported in the overparametrized regime. In view of the classical bias-variance trade-off, this behaviour is highly counterintuitive. The talk summarizes recent theoretical results on overparametrization and the bias-variance trade-off. This is joint work with Alexis Derumigny (Delft).

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Tuesday, 01.11.2022, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Alexandra Suvorikova, WIAS Berlin:
Robust k-means clustering (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
In this work we investigate the theoretical properties of robust k-means clustering under assumption of adversarial data corruption. We provide non-asymptotic rates for excess distortion under weak model assumptions on the moments of the distribution.

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Wednesday, 26.10.2022, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Kerrek Stinson, Universität Bonn:
A gradient flow perspective for weak solutions of the Mullins--Sekerka flow and an application to lithium-ion batteries (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
The purpose of this talk is to develop a gradient flow perspective for the Mullins--Sekerka equation, intrinsic to the evolving surface, at the level of a weak solution theory. The solution concept is motivated by the De Giorgi framework for curves of maximal slope and consideration of Gamma-convergence for gradient flows in the spirit of Sandier and Serfaty. Solutions must satisfy an optimal energy dissipation relation, where both the time derivative and metric slope are considered with respect to formal tangent spaces, arising from the mass preserving normal velocities. We prove that such solutions exist, may be recast in a PDE sense, and subsume the solution concept introduced by Le in the study of Gamma-convergence for the Cahn--Hilliard equation. As an application, we explore how a related solution concept can be used to understand the sharp interface limit of the Cahn--Hilliard reaction model for phase separation in lithium-ion batteries. Joint works with Sebastian Hensel (U. Bonn) and Tim Laux (U. Bonn).

Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 25.10.2022, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Luca Pelizzari, WIAS Berlin:
Polynomial Volterra processes and rough polynomial models (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
October 24 – 26, 2022 (Novotel Berlin Mitte)
Workshop/Konferenz: SPP 1962 Annual Meeting 2022
more ... Location
Novotel Berlin Mitte

Host
WIAS Berlin
DFG Schwerpunktprogramm 1962
Wednesday, 19.10.2022, 14:30 (WIAS-405-406)
Seminar Interacting Random Systems
Nicolas Forien, Sapienza Università di Roma, Italien:
Sleepy frogs playing ping-pong on an overcrowded torus: The supercritical phase of Activated Random Walks
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
Consider, on each site of a graph, a certain number of frogs (or particles) which can be either active or sleeping. Each active frog performs a continuous-time random walk and falls asleep with a certain rate. Sleeping frogs stop moving, until they wake up when another frog arrives on the same site. This model on Z^d presents a phase transition: depending on the density of frogs (initially all active) and on the sleep rate, either almost surely each frog eventually falls asleep forever (fixating phase), or almost surely no frog falls asleep forever (active phase). In this talk, I will present a very recent work with Amine Asselah and Alexandre Gaudillière (arxiv.org/abs/2210.04779) about the critical density separating the two phases, showing that it is stricly below 1 for whatever value of the sleep rate. Skipping the technical details, the proof is quite geometric and intuitive, simply consisting of teams of frogs which play battles of coloured loops...

Further Informations
Seminar Interacting Random Systems

Host
WIAS Berlin
Wednesday, 19.10.2022, 11:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. David Frazier, Monash University, Australien:
Guarenteed robustness via semi-modular posterior inference (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Even in relatively simple settings, model misspecification can cause Bayesian inference methods to fail spectacularly. In situations where the underlying model is built by combining different modules, an approach to guard against misspecification is to employ cutting feedback methods. These methods modify conventional Bayesian posterior inference algorithms by artificially limiting the information flows between the (potentially) misspecified and correctly specified modules. By artificially limiting the flow of information when updating our prior beliefs, we essentially "cut" the link between these modules, and ultimately produce a posterior that differs from the exact posterior. However, it is generally unknown when one should prefer this "cut posterior" over the exact posterior. Rather than choosing a single posterior on which to base our inferences, we propose a new Bayesian method that combines both posteriors in such a way that we can guard against misspecification, and decrease posterior uncertainty. We derive easily verifiable conditions under which this new posterior produces inferences that are guaranteed to be more accurate than using either posterior by itself. We demonstrate this new method in a host of applications.

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Wednesday, 19.10.2022, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. Ottmar Cronie, Chalmers University of Technology & University of Gothenburg, Schweden:
Point process learning: A cross-validation-based approach to statistics for point processes (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Point processes are random sets which generalise the classical notion of a random (iid) sample by allowing i) the sample size to be random and/or ii) the sample points to be dependent. Therefore, point process have become ubiquitous in the modelling of spatial and/or temporal event data, e.g. earthquakes and disease cases. Motivated by cross validation's general ability to reduce overfitting and mean square error, in this talk, we present a new cross-validation-based statistical theory for general point processes. It is based on the combination of two novel concepts for general point processes: cross validation and prediction errors. Our cross-validation approach uses thinning to split a point process/pattern into pairs of training and validation sets, while our prediction errors measure discrepancy between two point processes. The new statistical approach exploits the prediction errors to measure how well a given model predicts validation sets using associated training sets. Due to its connection to the general idea of empirical risk minimisation, it is referred to as Point Process Learning. We discuss properties of the proposed approach and its components, and we illustrate how it may be applied in different spatial statistical settings. In (at least) one of these settings, we numerically show that it outperforms the state of the art.

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Tuesday, 18.10.2022, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Egor Gladin, Humboldt Universität zu Berlin:
Algorithm for constrained Markov decision process with linear convergence (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
The problem of constrained Markov decision process is considered. An agent aims to maximize the expected accumulated discounted reward subject to multiple constraints on its costs (the number of constraints is relatively small). A new dual approach is proposed with the integration of two ingredients: entropy-regularized policy optimizer and Vaidya's dual optimizer, both of which are critical to achieve faster convergence. The finite-time error bound of the proposed approach is provided. Despite the challenge of the nonconcave objective subject to nonconcave constraints, the proposed approach is shown to converge (with linear rate) to the global optimum. The complexity expressed in terms of the optimality gap and the constraint violation significantly improves upon the existing primal-dual approaches.

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Friday, 14.10.2022, 14:00 (WIAS-Library)
E-Coffee-Lecture
Thomas Bender, WIAS:
Visual & Communication Design: Dos and Don'ts
more ... Location
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411

Host
WIAS Berlin
Thursday, 13.10.2022, 10:15 (WIAS-HVP-3.13)
Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Michael Multerer, Università della Svizzera italiana, Schweiz:
Samplets: Construction and scattered data compression
more ... Location
Weierstraß-Institut, Hausvogteiplatz 11A, 10117 Berlin, 3. Etage, Raum: 3.13

Host
WIAS Berlin
Wednesday, 12.10.2022, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Arne Grauer, Universität zu Köln:
Short paths in scale-free geometric random graphs
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
We study the occurence of ultrasmallness in geometric random graphs defined on the points of a Poisson process in d-dimensional space, which additionally carry independent random marks. In our framework, edges are established at random using the marks of the endpoints and the distance between points in a flexible way such that a large class of graph models with scale-free degree distribution and edges spanning large distances is included. We give a sharp criteria for the absence of ultrasmallness of the graphs and in the ultrasmall regime establish a limit theorem for the chemical distance of two points. Here, the boundary of the ultrasmall regime and the limit theorem depend not only on the power-law exponent of the graphs but also on a geometric quantity, the influence of the spatial distance of two typical points on the probability of an edge connecting them. Furthermore, we study the contact process on these random graphs in the ultrasmall regime and provide exact asymptotics for the non-extinction proba- bility when the rate of infection spread is small. The talk is based on joint work with Peter Gracar and Peter Mörters.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Tuesday, 11.10.2022, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Anja Schlömerkemper, Julius-Maximilians-Universität Würzburg:
A discussion of two models extending the Cahn--Hilliard equation to a temperature-dependent setting (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
The dynamics of binary media can be modeled by the Cahn--Hilliard equation. Sometimes the phase separation depends crucially on the temperature. I will discuss two models introduced in joint work with Francesco De Anna, Chun Liu and Jan-Eric Sulzbach, arXiv:2112.14665. The models are obtained by combining ideas from non-equilibrium thermodynamics with an energetic variational approach and taking the transport property of the temperature into account. I will discuss selection criteria for these models and provide some analytical results regarding well-posedness of one of the models.

Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Thursday, 29.09.2022, 16:00 (Online Event)
Seminar Materialmodellierung
Prof. Dr. Robert Eisenberg, Rush University, USA:
From Maxwell to Mitochondria (online talk)
more ... Location
Online Event

Further Informations
Seminar Materialmodellierung

Host
WIAS Berlin
Wednesday, 28.09.2022, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Willem van Zuijlen, WIAS:
Weakly self-avoiding walk in a random potential
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
We investigate a model of simple-random walk paths in a random environment that has two competing features: an attractive one towards the highest values of a random potential, and a self-repellent one in the spirit of the well-known weakly self-avoiding random walk. We tune the strength of the second effect such that they both contribute on the same scale as the time variable tends to infinity. In this talk I will discuss our results on the identification of (1) the logarithmic asymptotics of the partition function, and (2) of the path behaviour that gives the overwhelming contribution to the partition function. This is joint work with Wolfgang König, Nicolas Pétrélis and Renato Soares dos Santos.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Wednesday, 28.09.2022, 11:00 (Online Event)
Seminar Weierstrass Group Data-Driven Optimization and Control
Jia Wang, Peking University, China, Volksrepublik:
Performance optimization of model predictive control algorithm and its application (online talk)
more ... Location
Online Event

Abstract
Abstract: The talk includes three main topics: (1) In order to accelerate the quadratic programming of linear MPC problem, a new iterative parameter selection method is proposed, which extends the existing proximal gradient method to high-order convergence rate. The proposed method uses the unique positive real root of a special set of higher-order polynomial equations as the iterative parameter. It can be shown that the selected polynomial order is the order of the convergence rate, so as to achieve a faster speed. (2) In order to overcome the slow convergence speed of traditional distributed MPC calculation, a novel iterative solution is proposed, which generates the next step solution according to the iterative error and error gain matrix. The iterative error is augmented to the traditional calculation process, then the new iterative formula is regarded as a nonlinear system. The convergence condition is derived by using the linear matrix inequality. Finally, the fast convergence is achieved by optimizing the error gain matrix. (3) For the economic predictive control of nonlinear systems, this study proposes an optimization method to achieve the global optimal approximation, which overcomes the deficiency that the existing MPC can only achieve local optimum. By estimating the suboptimal degree of the traditional MPC and modifying the control law according to the estimation results, the economic performance of the system is improved to approach the global optimum.

Further Informations
Seminar of Weierstrass Group DOC

Host
WIAS Berlin
Tuesday, 27.09.2022, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
PhD Mao Fabrice Djete, Université Paris Dauphine , Frankreich:
Non-regular McKean--Vlasov equations and calibration problem in local stochastic volatility models (online talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
In this talk, motivated by the calibration problem in local stochastic volatility models, we will investigate some McKean--Vlasov equations beyond the usual requirement of continuity of the coefficients in the measure variable for the Wasserstein topology. We will provide first an existence result for this type of McKean?Vlasov equations and explain the main idea behind the proof. In a second time, we will show an approximation by particle system for this type of equations, a result almost never rigorously proven in the literature in this context.

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Tuesday, 27.09.2022, 15:00 (WIAS-ESH)
Seminar Laserdynamik
Prof. Dmitry Turaev, Imperial College London, UK:
Non-ergodicity and stable coherent motions in systems of mutually repelling particles with arbitrarily high kinetic energy
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Seminar Laser Dynamics

Host
WIAS Berlin
Monday, 19.09.2022, 13:30 (Online Event)
Seminar Materialmodellierung
Prof. Robert Jack, University of Cambridge, GB:
Examples of hydrodynamic behaviour in two-species exclusion processes (online talk)
more ... Location
Online Event

Abstract
We discuss several different results for simple exclusion processes with two species of particles. We first show numerical results where inhomogeneous states appear in two-dimensional systems where the species are driven in opposite directions, and we explain how these results can be rationalised by considering hydrodynamic PDEs for the density [1]. We then discuss how hydrodynamic equations in such models can be characterised, including a systematic analysis based on the method of matched asymptotics [2]. Finally, I will present some results [3] for large deviations in the hydrodynamic limit, associated with fluctuations of the entropy production in a simple model of active matter [4]. [1] H. Yu, K. Thijssen and R. L. Jack, arXiv:2204.08863 [2] J. Mason, R. L. Jack, and M. Bruna, arXiv:2203.01038. [3] T. Agranov, M. E. Cates and R. L. Jack, in preparation. [4] M. Kourbane-Houssene, C. Erignoux, T. Bodineau and J. Tailleur, Phys. Rev. Lett., 120, 268003 (2018).

Further Informations
Seminar Materialmodellierung

Host
WIAS Berlin
Tuesday, 13.09.2022, 11:30 (WIAS-406)
Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Alfred Schmidt, Universität Bremen:
Multi scale models for a tool grinding process
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Host
WIAS Berlin
Tuesday, 13.09.2022, 10:15 (WIAS-406)
Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Dr. André Massing, NTNU Trondheim, Norwegen:
CutFEM: Discretizing geometry and partial differential equations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Host
WIAS Berlin
September 12 – 14, 2022 (WIAS-ESH)
Workshop/Konferenz: Mathematical Models for Biological Multiscale Systems (Hybrid Event)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
The workshop MathBio22 - Mathematical models for biological multiscale systems discusses and identifies mathematical methods that bridge the gap in scale and complexity between microscopic descriptions of biological and biophysical systems with corresponding PDE descriptions. The focus is on the multi-scale nature innate to biological processes connecting interacting biomolecules with complex systems such as cells, tissue, and organs to elucidate macroscopic phenomena, e.g., (cross)diffusion, liquid-liquid phase separation, gelation, growth. The corresponding model hierarchies require innovative and structure-preserving numerical methods, novel simulation techniques, and new analytical tools for the resulting nonlinear PDE systems. The latter concerns in particular questions of well-posedness, long-term behavior, qualitative properties of solutions, and coupling to microscopic, stochastic, or agent-based models. Variational and energy- or entropy-based methods are of particular interest.

Host
WIAS Berlin
Thursday, 08.09.2022, 14:00 (WIAS-ESH)
Seminar Numerische Mathematik
Dr. Yiannis Hadjimichael, WIAS Berlin:
Implicit strong-stability-preserving Runge--Kutta methods with downwind-biased operators
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Strong stability preserving (SSP) time integrators have been developed to preserve certain nonlinear stability properties (e.g., positivity, monotonicity, boundedness) of the numerical solution in arbitrary norms, when coupled with suitable spatial discretizations. The existing general linear methods (including Runge-Kutta and linear multistep methods) either attain small time steps for strong stability preservation or are only first-order accurate. One way to relax the time-step restrictions is to consider time integrators that contain both upwind- and downwind-biased operators.
In this talk, we review SSP Runge-Kutta methods that use upwind- and downwind-biased discretizations in the framework of perturbations of Runge-Kutta methods. We show how downwinding improves the SSP properties of time-stepping methods and breaks some stability barriers. In particular, we focus on implicit downwind SSP Runge-Kutta methods whose SSP coefficient can vary with respect to the method's coefficients. We present a novel one-parameter family of third-order, three-stage perturbed Runge-Kutta methods, for which the CFL-like time-step restriction can be arbitrarily large. The stability of this family of methods is analyzed, and we demonstrate that such methods are accurate enough when large CFL numbers are used. Furthermore, we discuss the complexity of solving the nonlinear problem at each step and we propose a block factorization of the Jacobian that reduces the computational cost of Newton's method.

Further Informations
For zoom login details please contact Ulrich Wilbrandt ulrich.wilbrandt@wias-berlin.de

Host
WIAS Berlin
Tuesday, 30.08.2022, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Adéline Fermanian, Mines ParisTech, France:
Framing RNN as a kernel method: A neural ODE approach (online talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
Building on the interpretation of a recurrent neural network (RNN) as a continuous-time neural differential equation, we show, under appropriate conditions, that the solution of a RNN can be viewed as a linear function of a specific feature set of the input sequence, known as the signature. This connection allows us to frame a RNN as a kernel method in a suitable reproducing kernel Hilbert space. As a consequence, we obtain theoretical guarantees on generalization and stability for a large class of recurrent networks. Our results are illustrated on simulated datasets.

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
August 30, 2022 (WIAS-ESH)
Workshop/Konferenz: Symposium on occasion of Uwe Bandelow's 60th anniversary
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We will organize at WIAS a Symposium on occasion of Uwe Bandelow's 60th anniversary. After the scientific program there will be also a session where you are invited to deliver personal or official greetings, share your memories, or present gifts. For guests who are unable to participate in person, the event will be available in a zoom meeting.

Host
WIAS Berlin
August 22 – 26, 2022 (Harnack-Haus)
Workshop/Konferenz: Stochastic & Rough Analysis
more ... Location
Harnack-Haus -- Tagungsstätte der Max-Planck-Gesellschaft

Host
Freie Universität Berlin
Humboldt-Universität zu Berlin
Technische Universität Berlin
Universität Potsdam
WIAS Berlin
Tuesday, 16.08.2022, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Prof. Mathias Staudigl, Maastricht University, Niederlande:
Stochastic relaxed inertial forward-backward-forward splitting for monotone inclusions in Hilbert spaces (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Tuesday, 02.08.2022, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr Vaios Laschos, WIAS Berlin:
Risk-sensitive partially observable Markov decision processes as fully observable multivariate utility optimization problems (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Thursday, 21.07.2022, 14:00 (Online Event)
Seminar Numerische Mathematik
Prof. Gabriel Acosta, University of Buenos Aires, Argentinien:
Nonlocal models related problems
more ... Location
Online Event

Abstract
abstract

Further Informations
For zoom login details please contact ulrich.wilbrandt@wias-berlin.de

Host
WIAS Berlin
July 21, 2022 (Online Event)
Workshop/Konferenz: Minisymposium for Young Researchers 2022
more ... Location
Online Event

Abstract
The "Minisymposium for Young Researchers 2022" (MSYR22) will bring together young scientists in the field of nonlinear optics and photonics. The minisymposium is related to the main workshop "Nonlinear Waves and Turbulence in Photonics" (NWTP22). The guiding idea is to provide an international platform which leads to a more comprehensive understanding of fundamental nonlinear phenomena, such as wave-turbulence, solitons, and extreme waves. The conference is fully online and available via Zoom. The link will be sent per E-Mail to the participants shortly before the conference's beginn.

Host
WIAS Berlin
Wednesday, 20.07.2022, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Nikita Simonov, LaMMe-Universitè d'Évry Val d'Essone, France:
Fast diffusion equations, tails and convergence rates
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Understanding the intermediate asymptotic and computing convergence rates towards equilibria are among the major problems in the study of parabolic equations. Convergence rates depend on the tail behaviour of solutions. This observation raised the following question: how can we understand the tail behaviour of solutions from the tail behaviour of the initial datum? In this talk, I will discuss the asymptotic behaviour of solutions to the fast diffusion equation. It is well known that non-negative solutions behave for large times as the Barenblatt (or fundamental) solution, which has an explicit expression. In this setting, I will introduce the Global Harnack Principle (GHP), precise global pointwise upper and lower estimates of non-negative solutions in terms of the Barenblatt profile. I will characterize the maximal (hence optimal) class of initial data such that the GHP holds by means of an integral tail condition. As a consequence, I will provide rates of convergence towards the Barenblatt profile in entropy and in stronger norms such as the uniform relative error.

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 13.07.2022, 12:30 (WIAS-405-406)
Seminar Interacting Random Systems
Quirin Vogel, NYU Shanghai, China, Volksrepublik:
The variational principle and the Bose gas
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
Variational principles often occur in large deviation theory, the most prominent example being the Varadhan lemma. Gibbs measures are often a canonical candidate for minimizers. In this talk, we will construct Gibbs measures for the interacting Bose gas and check under which circumstances they may solve certain minimization problems. This is work in progress, so a fair number of conjectures will be introduced. Joint work with Tianyi Bai, also from NYU Shanghai.

Further Informations
Seminar Interacting Random Systems

Host
WIAS Berlin
July 13 – 15, 2022 (WIAS-ESH)
Workshop/Konferenz: Nonlinear Waves and Turbulence in Photonics 2022
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
The workshop "Nonlinear Waves and Turbulence in Photonics" (NWTP22) will bring together leading experts in the field of nonlinear optics and photonics. The workshop's guiding idea is to provide an international platform which leads to a more comprehensive understanding of fundamental nonlinear phenomena, such as wave-turbulence, solitons, and extreme waves. We expect exciting reports and fruitful discussions both on the most recent advances in the field and promising future developments.

Host
WIAS Berlin
Tuesday, 12.07.2022, 13:30 (WIAS-ESH)
Seminar Numerische Mathematik
Dr. Zahra Lakdawala, Lahore University of Management Sciences, Pakistan:
On water wave dynamics using physics informed neural networks
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
A vanilla feed forward neural network consists of neurons and layers and the mapping between input and output is approximated using a non-linear function. The network is trained using data. In this work, we set up a neural network such that the spatio-temporal solution of time-dependent wave propagation models is learnt. This is done by providing the physical model, such as the 1D wave and shallow water wave equations and its associated boundary and initial conditions, as rules for learning the network. We investigate the feasibility of data-driven and model-driven network predictions against numerical solutions. We further investigate the accuracy of the trained network through different parameter configurations and look closely into the multi-objective loss function that is constructed by including the residual error of the physical equations and the associated initial and boundary conditions. We present the results of numerical solutions against solutions obtained from data and model-driven neural networks using data and physics informed rules for learning. Lastly, we construct a hybrid data and physics driven network and show that this significantly improves the accuracy of the physics-driven network.

Host
WIAS Berlin
Tuesday, 05.07.2022, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Alexander Marx, WIAS Berlin:
Random interactions in the mean-field Ising model (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
July 5 – 8, 2022 (WIAS-ESH)
Workshop/Konferenz: Workshop on Numerical Methods and Analysis in CFD
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin
Wednesday, 29.06.2022, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Stefanie Schindler, WIAS Berlin:
Entropy method for a coupled reaction-diffusion system on the real line (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In this talk, we investigate the long-time behavior of solutions to a nonlinear coupled reaction-diffusion system with detailed balance on the real line. By assuming that the solutions are in equilibria at infinity, we study the convergence towards a self-similar profile, which is a generalized steady-state in parabolic scaling variables. With this convergence, we answer how the solutions to the system mix the two stable asymptotic boundary values when time increases. Our strategy is to use an entropy approach with the relative Boltzmann entropy functional. This is a standard method for reaction-diffusion systems of mass-action type on bounded domains and a meaningful alternative to the linearization around an equilibrium. While this approach is well-studied on bounded domains, things become more complicated on the whole real line. This research is joint work with Alexander Mielke.

Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.

Host
Humboldt-Universität zu Berlin
WIAS Berlin
June 29 – July 1, 2022 (Harnack-Haus)
Workshop/Konferenz: Random Point Processes in Statistical Physics
more ... Location
Harnack-Haus -- Tagungsstätte der Max-Planck-Gesellschaft

Host
WIAS Berlin
DFG Schwerpunktprogramm 2265
Wednesday, 29.06.2022, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. Anuj Srivastava, Florida State University, USA:
Statistical shape analysis of complex natural structures (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Shape analysis of structured data is a fast-growing field with broad applications. Advances in imaging techniques have led to a rich data source for analyzing shapes across many scientific disciplines. Examples include shapes of brain structures; morphological analysis of cancer cells, leaves, or botanical trees; shapes of geographical objects; human biometrics; shapes of the human genome; and so on. Shapes are relevant even in non-imaging data contexts, e.g., the shapes of COVID rate curves or the shapes of breathing pat- terns in sleep studies. What makes shape analysis both fascinating and challenging? The main difficulty stems from the fact that shape is generally an abstract notion that is hard to quantify. Imposing statistical models and inferences on shapes seem even more daunting. I will outline developments in a particular approach called elastic shape analysis. This approach defines shape as a quantity left after the effects of so-called nuisance transformations (often translations, rotations, and parameterizations) are removed. This removal requires representations and metrics that are invariant to these transformations. Elastic Riemannian metrics provide desired invariances but can be cumberso- me in practical implementations. A family of square-root type transformations has helped simplify these computations and make this approach feasible. These geometrical tools help us compute average shapes of 3D (botanical) trees, develop a shape alphabet for representing chromosomes as letter sequences, perform principal component analysis of arterial brain networks, and model dynamics of Entamoeba Histolytica in different liquid media. Furthermore, they help us address some fundamental scientific questions: Are the shapes of mitochondria in muscle tissues affected by the lifestyle (active versus sedentary)? Can we predict the onset of cognitive disorders using subcortical structures in the human brain? How does aging affect morphologies of arterial networks in human brains? I will present some of these applications of elastic shape analysis

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Universität Potsdam
Tuesday, 28.06.2022, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Karsten Tabelow, WIAS Berlin:
In-vivo tissue properties from magnetic resonance data (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Friday, 24.06.2022, 13:00 (Online Event)
E-Coffee-Lecture
Henrik Pletat/Andrej Fink, WIAS IT Dep.:
Services of the WIAS IT-Department
more ... Location
Online Event

Host
WIAS Berlin
Thursday, 23.06.2022, 14:00 (WIAS-ESH)
Seminar Materialmodellierung
Dr. Giovanni Ligorio, Humboldt-Universität zu Berlin:
Neuromorphic device development: From modification of surfaces to modification of functions (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
The versatility offered by organic molecules and polymers holds great functional and economic potential for optoelectronic devices. The chemical modification of electrodes with organic materials is a common approach in our group for tuning the electronic landscape between interlayers in devices, thus facilitating charge carrier injection/extraction and improving device performance. A common tool to modify the electrode interfaces is to use covalently bound molecules carrying a permanent electric dipole group. Beside employing molecules with constant dipole, we also investigated the possibility to use switchable photochromic molecules which undergo structural modification when illuminated with light. This allows a dynamic and reversable control of the electronic properties. The gained control over the device performance enables additional functionalities in devices, such as neuromorphic applications. Neuromorphic engineering takes inspiration from the functionalities and structure of the brain to solve complex tasks and enable learning. Yet, hardware realization that simulates the synaptic activities realized with electrical devices is still not as advanced as the common implementation in computer software. In my talk I will present different approaches to emulate synapses and to fabricate both (i) optical and (ii) electronic synaptic devices. The first (i) were achieved by employing the above-mentioned photochromic molecules. This allowed control of the optical properties of gold films by reversibly modulating the surface plasmon resonance. The second (ii) were achieved by fabricating two-terminal devices based on mixed ionic-electronic conducting polymers that serve as active layer for ions and charge carrier conduction. The precise understanding and modeling of device functions will allow to fully exploit the potential of these synthetic synapses. For this purpose, a mathematical description of their behaviour might allow to move from single devices to networks and enable in materia computing.

Further Informations
Hybrid Event - please take into consideration that the number of on-site participants is limited to 24.

Host
WIAS Berlin
Wednesday, 22.06.2022, 12:30 (WIAS-405-406)
Seminar Interacting Random Systems
Lukas Lüchtrath, Universität zu Köln:
The various phases of long-range inhomogeneous percolation
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
We consider a large class of inhomogeneous spatial random graphs where the vertex set is given by a Poisson process in Euclidean space and each vertex carries additionally an i.i.d. weight. Edges are drawn in such a way that short edges and edges to large-weight vertices are preferred. This allows in particular the study of models that combine long-range interactions and heavy-tailed degree distributions. The occurrence of long edges together with the hierarchy of the vertices coming from the weights typically leads to very well connected graphs. We identify a sharp phase transition where the existence of a subcritical percolation phase becomes impossible. This transition depends on both the power law of the degree distribution and on the geometric model parameter, showing the significant effect of clustering on the graph?s topology. We consider afterwards the specifics of dimension one in parameter regimes where a subcritical phase exists. Due to the geometric restrictions of the line, it is fairly hard to generate infinite clusters in this case and many established models admit no supercritical phase. We identify sharply how the combination of weights and long-range effects can lead to infinite clusters in situations where both effects alone are not strong enough for an infinite cluster to exist. Natural examples that are contained in our framework are for instance the random connection model, the Poisson Boolean model, scale-free percolation, the age-dependent random connection model and their soft versions. Joint work with Peter Gracar, Christian Mönch and Peter Mörters.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Monday, 20.06.2022, 16:00 (WIAS-ESH)
Seminar Numerische Mathematik
Prof. Maxim A. Olshanskii, University of Houston, USA:
Numerical analysis of surface fluids
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In this talk we focus on numerical analysis for systems of PDEs governing the motion of material viscous surfaces, the topic motivated by continuum-based modeling of lateral organization in plasma membranes. We shall consider several systems of fluid and phase-field equations defined on evolving surfaces and discuss some recent results about well-posedness of such problems. We further introduce a computational approach and numerical analysis for the resulting systems of PDEs. The methods are combined to deliver a computationally tractable and thermodynamically consistent model describing the dynamics of a two-phase viscous layer. The talk closes with an illustration of the model capacity to predict lateral ordering in multicomponent vesicles of different lipid compositions.

Host
WIAS Berlin
Wednesday, 15.06.2022, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. Dr. Alexandra Carpentier, Universität Potsdam:
Optimal ranking for crowd-sourcing (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 14.06.2022, 15:15 (WIAS-ESH)
Oberseminar Nonlinear Dynamics
Dr. Babette de Wolff, Vrije Universiteit, Netherlands:
Delayed feedback stabilization & unconventional symmetries (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In 1992, the physicist Pyragas proposed a time delayed feedback scheme to stabilize periodic solutions of ordinary differential equations. The feedback scheme (now known as `Pyragas control?) has been adapted to symmetric systems whose symmetries can be described by groups. In this talk, we explore how Pyragas control can be adapted to systems with `unconventional symmetries?, i.e. symmetries that cannot be described by groups. In the first part of the talk, we review a fundamental observation that gives insight in Pyragas control without symmetry. In the second part of the talk we give an example of a system of three coupled oscillators with `unconventional symmetries?. For this example, we discuss what a Pyragas-like control scheme looks like and what the stabilization properties of this control scheme are. The first part of the talk based on joint work with Isabelle Schneider (FU Berlin/Universität Rostock); the second part of the talk is based on joint work with Bob Rink (VU Amsterdam)

Further Informations
Oberseminar Nonlinear Dynamics

Host
Freie Universität Berlin
WIAS Berlin
Tuesday, 14.06.2022, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Priv. - Doz. Dr. John Schoenmakers, WIAS Berlin:
Dual randomization and empirical dual optimization for optimal stopping (online talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Wednesday, 08.06.2022, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Robert Lasarzik, WIAS Berlin:
Energy-variational solutions and their approximation (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In this talk, energy-variational (EnVar) solutions are introduced for a large class of nonlinear evolution equations. Considering the Ericksen--Leslie equations modelling the evolution of liquid crystals, we observe that EnVar solutions emerge as the limit of a structure-preserving finite element scheme. We can show weak-strong uniqueness of the limit solution and additionally the so-called semi-flow property, which says that concatenations and restrictions of EnVar solutions are EnVar solutions again. Under certain assumptions every EnVar solution implies the existence of a measure-valued solution to the Ericksen--Leslie system. This implies that the EnVar solution concept is finer than the usual measure-valued solution concept. Finally, a time-discretization scheme is introduced via an incremental minimization, which resembles the minimizing movement scheme for gradient flows.

Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 08.06.2022, 10:00 (Online Event)
Forschungsseminar Mathematische Statistik
PhD Mari Myllymäki, Natural Resources Institute Finland (Luke):
Global envelopes with applications to spatial statistics and functional data analysis (online talk)
more ... Location
Online Event

Abstract
Global envelopes are nowadays quite often used in testing null models for spatial processes by means of different summary functions, because they provide a formal test and provide suggestions for alternative models through graphical interpretation of the test results. Global envelopes are however a rather general tool that can be applied in various applications. Namely, they can be employed for central regions of functional or multivariate data, for graphical Monte Carlo and permutation tests where the test statistic is multivariate or functional, and for global confidence and prediction bands. In this talk, I describe the global envelopes, illustrate the methodology on different applications including the functional general linear model and show examples of the usage of the R package GET (Myllymäki and Mrkvička, 2020) that implements global envelopes. Further, I discuss the multiple testing correction in the global envelope tests for functional test statistics, which are discretized to m highly correlated hypotheses. While the global envelopes were first developed to control the family-wise error rate, also control of false discovery rate can be introduced. Myllymäki and Mrkvička (2020). GET: Global envelopes in R. arXiv:1911.06583 [stat.ME] htt- ps://arxiv.org/abs/1911.0658

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 07.06.2022, 10:15 (WIAS-ESH)
Seminar Nichtlineare Optimierung und Inverse Probleme
Dr. Pedro Pérez-Aros, Universidad de O'Higgins, Chile:
Inner Moreau envelope of nonsmooth conic chance constrained optimization problems
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin
Thursday, 02.06.2022, 16:00 (WIAS-ESH)
Forschungsseminar Mathematische Modelle der Photonik
Fenja Severing, WIAS Berlin:
Instabilities in the context of the Generalized Nonlinear Schrödinger Equation
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Tba

Further Informations
Forschungsseminar Mathematische Modelle der Photonik

Host
WIAS Berlin
Thursday, 02.06.2022, 14:00 (WIAS-ESH)
Seminar Numerische Mathematik
Julien Moatti, Université de Lille, Frankreich:
A structure preserving hybrid finite volume scheme for semi-conductor models on general meshes
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In 1996, Gajewski and Gärtner introduced a model describing semi-conductor devices in presence of an exterior magnetic field and proposed a scheme to discretise it. From a numerical point of view, the main difficulty in dealing with this model is the impact of the magnetic field over the system, which leads to anisotropic diffusion equations. In particular their scheme does not preserve the positivity of the solutions if the magnetic field is too intense.
In this talk, I will introduce a new structure preserving scheme for discretising similar systems of equations. The scheme under study is based on the Hybrid Finite Volume method, which is devised to handle anisotropic diffusion tensors alongside with very general polygonal/polyhedral meshes. It is designed to handle general statistics (including Boltzmann and Blakemore) as well as strong magnetic fields, while ensuring that the computed densities are positive.
The analysis of the scheme relies on the preservation of an entropy structure at the discrete level, which mimics the continuous behaviour of the system. I will explain how we can use this structure to show that there exist positive solutions to the scheme. As a by product, we also establish a "good discrete long-time behaviour" property: the discrete solutions converge towards a discrete thermal equilibrium as time tends to infinity.
Alongside with the theoretical results, I will present numerical results obtained with this scheme in various situations. I will especially focus on the preservation of bounds for the carrier densities and on the long-time behaviour of the solutions.
This is a joint work with Claire Chainais-Hillairet, Maxime Herda and Simon Lemaire.

Host
WIAS Berlin
Wednesday, 01.06.2022, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Melanie Koser, Humboldt-Universität zu Berlin:
Pattern formation in certain frustrated spin systems (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 01.06.2022, 12:30 (WIAS-405-406)
Seminar Interacting Random Systems
Francesca Cottini, Università degli Studi di Milano-Bicocca, Italien:
Gaussian Limits for Subcritical Chaos
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
In this talk I will present a general and novel criterion to show the convergence towards a Gaussian limit for polynomial chaos, that is a multi-linear polynomial of independent random variables. This result is motivated by the study of 2d directed polymers in the subcritical regime and of the related 2d Stochastic Heat Equation, for which many convergence results were proved in recent years. Our criterion allows us to recover these results in a simpler way and, furthermore, to obtain novel results. I will focus on two main new Gaussian limits, for a singular product between the partition function and the disorder, and for the logarithm of the partition function, through an explicit chaos expansion. This is a joint work with Francesco Caravenna.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Tuesday, 31.05.2022, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Prof. Dr. Vladimir Spokoiny, WIAS Berlin:
Laplace's approximation in high dimension, Part 2 (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Tuesday, 31.05.2022, 13:30 (Online Event)
Seminar Materialmodellierung
Prof. Eric Sonnendrücker, Max-Planck-Institut für Plasmaphysik:
Geometric numerical methods for models from plasma physics (online talk)
more ... Location
Online Event

Abstract
Many kinetic and fluid plasma models, like the Vlasov--Maxwell-Landau or the Magnetohydrodynamics (MHD) models feature a Hamiltonian part that can be described by a Poisson bracket and a Hamiltonian and a dissipative part. The Hamiltonian part features in general different kinds of invariants that play a fundamental role in the evolution of the system. On the other hand the dissipative part strictly dissipates an entropy. For an accurate long time numerical simulation of these models, keeping as much as possible from the structure of the original equations is essential, which will automatically enforce the preservation of some important invariants like for example div B = 0. In this talk we will give an overview of structure preserving discretisation of such models based on Discrete Exterior Calculus. In particular we will show how a Particle In Cell discretisation of the Vlasov Equation coupled with a Finite Element Exterior Calculus discretisation for Maxwell's equations involving a discrete de Rham complex and an appropriate Finite Element approximation of each field leads to a Finite Dimensional Hamiltonian system, which then can be discretised in time with geometric integrators like Hamiltonian splitting or exact energy preserving discrete gradient methods.

Further Informations
Seminar Materialmodellierung

Host
WIAS Berlin
Tuesday, 31.05.2022, 13:30 (WIAS-ESH)
Seminar Numerische Mathematik
Dr. Gabriel R. Barrenechea, University of Strathclyde, GB:
Divergence-free finite element methods for an inviscid fluid model
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In this talk I will review some recent results on the stabilisation of linearised incompressible inviscid flows (or, with a very small viscosity).
The partial differential equation is a linearised incompressible equation similar to Euler's equation, or Oseen's equation in the vanishing viscosity limit. In the first part of the talk I will present results on the well-posedeness of the partial differential equation itself. From a numerical methods' perspective, the common point of the two parts is the aim of proving the following type of estimate:
u - _h^ _L^2^ leq C h^k+frac12 u _H^k+1^
where u is the exact velocity and u_h^ is its finite element approximation. In the estimate above, the constant C is independent of the viscosity (if the problem has a viscosity), and, more importantly, independent of the pressure. This estimate mimicks what has been achieved for stabilised methods for the convection-diffusion equation in the past. Nevertheless, up to the best of our knowledge, this is the first time this type of estimate is obtained in a pressure-robust way.
I will first present results of discretisations using H(div)-conforming spaces, such as Raviart-Thomas, or Brezzi-Douglas-Marini where an estimate of the type eqrefmain-estimate is proven (besides an optimal estimate for the pressure). In the second part of the talk I will move on to H^1-conforming divergence-free elements, with the Scott-Vogelius element as the prime example. In this case, due to the H^1-conformity, extra control on the convective term needs to be added. After a (very brief) review of the idea of vorticity stabilisation, I will present very recent results on CIP stabilisation where a discussion on the type, and number, of jump terms will be presented. The method is independent of the pressure gradients, which makes it pressure-robust and leads to pressure-independent error estimates such as eqrefmain-estimate.
Finally, some numerical results will be presented and the present approach will be compared to the classical CIP method.
This work is a collaboration with E. Burman (UCL, UK), and E. Caceres and J. Guzmán (Brown, USA).

Host
WIAS Berlin
Monday, 30.05.2022, 15:00 (Online Event)
Berlin Oberseminar: Optimization, Control and Inverse Problems
Prof. Pier Luigi Dragotti, Imperial College London, UK:
Computational imaging and sensing: Theory and applications (online talk)
more ... Location
Online Event

Abstract
The revolution in sensing, with the emergence of many new imaging techniques, offers the possibility of gaining unprecedented access to the physical world, but this revolution can only bear fruit through the skilful interplay between the physical and computational realms. This is the domain of computational imaging which advocates that, to develop effective imaging systems, it will be necessary to go beyond the traditional decoupled imaging pipeline where device physics, image processing and the end-user application are considered separately. Instead, we need to rethink imaging as an integrated sensing and inference model. In the first part of the talk we highlight the centrality of sampling theory in computational imaging and investigate new sampling modalities which are inspired by the emergence of new sensing mechanisms. We discuss time-based sampling which is connected to event-based cameras where pixels behave like neurons and fire when an event happens. We derive sufficient conditions and propose novel algorithms for the perfect reconstruction of classes of non-bandlimited functions from time-based samples. We then develop the interplay between learning and computational imaging and present a model-based neural network for the reconstruction of video sequences from events. The architecture of the network is model-based and is designed using the unfolding technique, some element of the acquisition device are part of the network and are learned with the reconstruction algorithm. In the second part of the talk, we focus on the heritage sector which is experiencing a digital revolution driven in part by the increasing use of non-invasive, non-destructive imaging techniques. These new imaging methods provide a way to capture information about an entire painting and can give us information about features at or below the surface of the painting. We focus on Macro X-Ray Fluorescence (XRF) scanning which is a technique for the mapping of chemical elements in paintings and introduce a method that can process XRF scanning data from paintings. The results presented show the ability of our method to detect and separate weak signals related to hidden chemical elements in the paintings. We analyse the results on Leonardo's 'The Virgin of the Rocks' and show that our algorithm is able to reveal, more clearly than ever before, the hidden drawings of a previous composition that Leonardo then abandoned for the painting that we can now see. This is joint work with R. Alexandru, R. Wang, Siying Liu, J. Huang and Y.Su from Imperial College London; C. Higgitt and N. Daly from The National Gallery in London and Thierry Blu from the Chinese University of Hong Kong.

Further Informations
Berlin Oberseminar: Optimization, Control and Inverse Problems

Host
WIAS Berlin
Technische Universität Berlin
Humboldt-Universität zu Berlin
Wednesday, 25.05.2022, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Joachim Rehberg, WIAS Berlin:
On non-autonomous and quasilinear parabolic systems (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 24.05.2022, 15:15 (WIAS-ESH)
Oberseminar Nonlinear Dynamics
Dr. Oleksandr A. Burylko, Institute of Mathematics NAS of Ukraine and Potsdam Institute for Climate Impact Research:
Symmetry breaking yields chimeras in two small populations of Kuramoto-type oscillators (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Despite their simplicity, networks of coupled phase oscillators can give rise to intriguing collective dynamical phenomena. However, the symmetries of globally and identically coupled identical units do not allow solutions where distinct oscillators are frequency-unlocked?a necessary condition for the emergence of chimeras. Thus, forced symmetry breaking is necessary to observe chimera-type solutions. Here, we consider the bifurcations that arise when full permutational symmetry is broken for the network to consist of coupled populations. We consider the smallest possible network composed of four phase oscillators and elucidate the phase space structure, (partial) integrability for some parameter values, and how the bifurcations away from full symmetry lead to frequency-unlocked weak chimera solutions Since such solutions wind around a torus they must arise in a global bifurcation scenario. Moreover, periodic weak chimeras undergo a period doubling cascade leading to chaos. The resulting chaotic dynamics with distinct frequencies do not rely on amplitude variation and arise in the smallest networks that support chaos

Further Informations
Oberseminar Nonlinear Dynamics

Host
WIAS Berlin
Freie Universität Berlin
Friday, 20.05.2022, 13:00 (Online Event)
E-Coffee-Lecture
Alireza Selahi Moghaddam, WIAS:
Creating nice 3d models and animations with Blender
more ... Location
Online Event

Abstract
Blender is an open source 3d modeling and animation software, which can easily compete with it's commercial counter-products. Although utilizing the full potential of such a software requires many years of learning, it is surprisingly easy to get nice results with very little effort, which can be used in scientific presentations or papers. With it's Python-interface, Blender even offers a way to fit right into the context of scientific computing.

Host
WIAS Berlin
Friday, 20.05.2022, 13:00 (Online Event)
Forschungsseminar Mathematische Modelle der Photonik
Prof. Andrey Shilnikov, Georgia State University, USA:
Long saga of in-depth modeling of two swim CPGs in two sea slugs (online talk)
more ... Location
Online Event

Abstract
We introduce the concepts underlying the modeling of swim CPGs of two sea slugs in control and under perturbations. The emphasis is put upon the nonlinear dynamics of both interacting cells and synapses and their synergy to produce an emergent network level bursting. We discuss some of its prominent features such feed back loops to maintain stability, including structural, as well resilience to short and long-term perturbations. Our research approaches are rooted in applied dynamical systems, parameter optimization with machine learning elements.

Further Informations
Forschungsseminar: Mathematische Modelle der Photonik

Host
WIAS Berlin
Wednesday, 18.05.2022, 15:15 (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
PD Dr. Maria Neuss-Radu, Friedrich-Alexander-Universität Erlangen-Nürnberg:
Effective models for nonlinear drift-diffusion of multiple species in porous media (online talk)
more ... Location
Online Event

Abstract
We consider a nonlinear drift-diffusion system for multiple charged species in a porous medium in 2D and 3D with periodic microstructure. The system consists of a transport equation for the concentration of the species and Poisson's equation for the electric potential. The diffusion terms depend nonlinearly on the concentrations. We consider non-homogeneous Neumann boundary condition for the electric potential. The aim is the rigorous derivation of an effective (homogenized) model in the limit when the scale parameter $epsilon$ tends to zero. This is based on uniform a priori estimates for the solutions of the microscopic model. The crucial result is the uniform $L^infty$-estimate for the concentration in space and time. This result exploits the fact that the system admits a nonnegative energy functional which decreases in time along the solutions of the system. By using weak and strong (two-scale) convergence properties of the microscopic solutions, effective models are derived in the limit $epsilon to 0$ for different scalings of the microscopic model. This is a joint work with Apratim Bhattacharya (Erlangen) and Markus Gahn (Heidelberg).

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 18.05.2022, 12:30 (WIAS-ESH)
Seminar Interacting Random Systems
Richard Kraaij, TU Delft:
Large deviations for weakly coupled slow-fast systems via the comparison principle of an associated Hamilton-Jacobi equation
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In statistical physics many interesting phenomena, e.g. behavior of systems at critical parameters or in the theory of hydrodynamic limits, arise from systems having multiple time-scales. A slow component is influenced by fast components, and as the number of interacting components tends to infinity, limiting results for the slow component are obtained in terms of 'averaged' versions of the fast components. I will consider in my talk the large deviations of coupled Markovian systems with two-time scales. The large deviations can arise from two sources: deviations of the slow process itself, or deviations of the large time averages of the fast process, effectively leading to a competition of two deviation effects. Arguing via the non-linear analogue of the "martingale problem approach" that applies for large deviations of Markov processes, we arrive at a uniqueness problem for a Hamilton-Jacobi-Bellman equation. We establish under mild conditions that this Hamilton-Jacobi-Bellman equation is well-posed, and as a consequence that we have a large deviation principle for a wide class of weakly coupled Markov processes.


Based on joint work with Mikola Schlottke (Eindhoven, The Netherlands)

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin

Wednesday, 18.05.2022, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Dr. Zdeněk Hlávka, Charles University, Tschechische Republik:
Testing dependencies in functional time series (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We discuss tests of serial independence for a sequence of functional observations and tests of independence between two (or more) time series of functional observations. The tests are based on characteristic functions which are appropriately estimated from functional observations. The limit distribution of the new test statistic is obtained under the null hypothesis, while under alternatives it is shown that the test statistics almost surely diverge as the sample size increases. In a Monte Carlo study, we investigate appropriate resampling methods and we investigate the tests? performance in finite samples. Finally, an application illustrates the use of the method with real data from financial markets, including also cumulative intraday returns of Bitcoin and Ethereum. References: Meintanis, S. G., Hušková, M., & Hlávka, Z. (2022). Fourier-type tests of mutual independence between functional time series. Journal of Multivariate Analysis, 189, 104873. Hlávka, Z., Hušková, M., & Meintanis, S. G. (2021). Testing serial independence with functional data. Test, 30(3), 603-629.

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 17.05.2022, 15:15 (WIAS-ESH)
Oberseminar Nonlinear Dynamics
Leonhard Schülen, Technische Universität Berlin:
The solitary route to chimera states
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We show how solitary states in a system of globally coupled FitzHugh-Nagumo oscillators can lead to the emergence of chimera states. By a numerical bifurcation analysis of a suitable reduced system in the thermodynamic limit we demonstrate how solitary states, after emerging from the synchronous state, become chaotic in a period-doubling cascade. Subsequently, states with a single chaotic oscillator give rise to states with an increasing number of incoherent chaotic oscillators. In large systems, these chimera states show extensive chaos. We demonstrate the coexistence of many of such chaotic attractors with different Lyapunov dimensions, due to different numbers of incoherent oscillators

Further Informations
Oberseminar Nonlinear Dynamics

Host
WIAS Berlin
Freie Universität Berlin
May 13 – 14, 2022 (HU Berlin HVP)
Workshop/Konferenz: 15th Annual ERC Berlin-Oxford Young Researchers Meeting on Applied Stochastic Analysis
more ... Location
Humboldt-Universität zu Berlin, Hausvogteiplatz 5-7, R. 0007

Host
Technische Universität Berlin
WIAS Berlin
May 12, 2022 (TUB-MA 415)
Workshop/Konferenz: 15th Annual ERC Berlin-Oxford Young Researchers Meeting on Applied Stochastic Analysis
more ... Location
Technische Universität, Straße des 17. Juni 136, 10623 Berlin, MA 415

Host
Technische Universität Berlin
WIAS Berlin
Wednesday, 11.05.2022, 15:15 (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Oğul Esen, Gebze Technical University, Türkei:
On geometry of Vlasov plasma (online talk)
more ... Location
Online Event

Abstract
This talk is about the Lie--Poisson formulation of Vlasov plasma. For the collisionless non-relativistic plasma motion, we shall introduce a system of differential equations called momentum-Vlasov equations. We shall show that this system is related to the Vlasov equation by a Poisson map. For the momentum-Vlasov equation, we shall propose a geometric pathway (involving complete lifts and vertical representatives) from the particle motion to the evolution of the field variables.

Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 11.05.2022, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. Dr. Vladimir Spokoiny, WIAS & HU Berlin:
Laplace approximation in high dimension with applications to statistical inference (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
This note revisits the classical results on Laplace approximation in a modern non-asymptotic and dimension free form. Such an extension is motivated by the uncertainty quantification for high dimensional statistical models. The established results provide an explicit non-asymptotic bounds on the quality of a Gaussian approximation of the posterior distribution in total variation distance in terms of the so called empheffective dimension p_G defined as interplay between information contained in the data and in the prior distribution. In the contrary to prominent Bernstein-von-Mises results, the impact of the prior is not negligible and it allows to keep the effective dimension small or moderate even if the true parameter dimension is huge or infinite. We also address the important issue of using a Laplace approximation with posterior mean in place of Maximum Aposteriori Probability (MAP).

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 10.05.2022, 16:30 (Online Event)
Oberseminar Nonlinear Dynamics
Dr. Yulia Petrova, Instituto de Matemática Pura e Aplicada, Brazil:
On the impact of dissipation ratio on vanishing viscosity solutions of Riemann problems for chemical flooding models (online talk)
more ... Location
Online Event

Abstract
We are interested in solutions of the Riemann problem arising in chemical flooding models for enhanced oil recovery (EOR). To distinguish physically meaningful weak solutions we use vanishing viscosity admissibility criterion. We demonstrate that when the flow function depends non-monotonically on the chemical agent concentration (which corresponds to the surfactant flooding), non-classical undercompressive shocks appear. They correspond to the saddle-saddle connections for the traveling wave dynamical system and are sensitive to precise form of the dissipation terms. In particular we prove the monotonic dependence of the shock velocity on the ratio of dissipative coefficients. The talk is based on joint work with F. Bakharev, A. Enin and N. Rastegaev (arxiv: 2111.15001).

Further Informations
Oberseminar Nonlinear Dynamics

Host
WIAS Berlin
Freie Universität Berlin
Tuesday, 10.05.2022, 15:15 (Online Event)
Oberseminar Nonlinear Dynamics
Prof. Dr. Sergey Tikhomirov, Instituto de Matemática Pura e Aplicada, Brazil:
Mixing zone in miscible displacement: application in polymer flooding and theoretical attempts of improving (online talk)
more ... Location
Online Event

Abstract
Injection of less viscous fluid to a more viscous one generates instabilities, which are often called “viscous fingers”. In case of miscible displacement it generates a mixing zone, where both fluids are presented. This phenomenon has a negative impact on flooding using chemical slugs in oil fields. We study the mathematical model describing the behavior on the rear front of a polymer slug. It consists of conservation of mass, incompressibility condition and Darcy law. This model often is called the Peaceman model. We study the size of the mixing zone appearing on the rear end of the polymer slug, provide pessimistic estimates and its numerical validation and apply estimates to the graded viscosity banks technology (GVB or tapering) to reduce the volume of used polymer without loss of effectiveness. Further optimization is possible with more delicate estimates of the mixing zone. In current work in progress with Yu. Petrova and Ya. Efendiev we consider a simplified model replacing multidimensional space with two tubes interacting with each other. In this system we numerically observe two traveling waves with different speeds. This behavior mimics the mixing zone of the multidimensional Pieceman model. We will speak on our progress in this direction.

Further Informations
Oberseminar Nonlinear Dynamics

Host
WIAS Berlin
Freie Universität Berlin
Tuesday, 10.05.2022, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Prof. Dr. Vladimir Spokoiny, WIAS & HU Berlin:
Laplace's approximation in high dimension (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Wednesday, 04.05.2022, 12:30 (WIAS-405-406)
Seminar Interacting Random Systems
Chengcheng Ling, TU Berlin:
Singular SDEs and PDEs
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
Well-posed stochastic differential equations with singular coefficients, as one of the known examples among 'regularization by noise' effect, are supported from the theoretical level mainly by the well-posedness results of parabolic PDEs with singular coefficients. In this talk we will discuss both sides: well-posedness of SDEs and PDEs with singular coefficients. Two examples will be shortly introduced in the end: numerical analysis and dynamical study of SDEs, which give us the partial image on how the equations are regularized by noise.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Wednesday, 04.05.2022, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Dr. Carlos Amendola, MPI Leipzig:
Likelihood geometry of correlation models (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Correlation matrices are standardized covariance matrices. They form an affine space of symmetric matrices defined by setting the diagonal entries to one. We study the geometry of maximum likelihood estimation for this model and linear submodels that encode additional symmetries. We also consider the problem of minimizing two closely related functions of the covariance matrix: the Stein's loss and the symmetrized Stein's loss. Unlike the Gaussian log-likelihood, these two functions are convex and hence admit a unique positive definite optimum. This is joint work with Piotr Zwiernik (University of Toronto).

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 03.05.2022, 15:15 (WIAS-ESH)
Oberseminar Nonlinear Dynamics
Dr. Marius Yamakou, Friedrich-Alexander-Universität Erlangen:
Transitions between weak-noise-induced resonance phenomena in a multiple timescales neural system
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We consider a stochastic slow-fast nonlinear dynamical system derived from a computational neuroscience model. Independently, we uncover the mechanisms that underlie two forms of weak-noise-induced resonance mechanisms, namely, self-induced stochastic resonance (SISR) and inverse stochastic resonance (ISR) in the system. We then show that SISR and ISR are related through the relative geometric positioning (and stability) of the fixed point and the generic folded singularity of the system's critical manifold. This result could explain the experimental observation in which real biological neurons with identical physiological features and stochastic synaptic inputs sometimes encode different information.

Further Informations
Oberseminar: Nonlinear Dynamics

Host
Freie Universität Berlin
WIAS Berlin
Tuesday, 03.05.2022, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Jun.-Prof. Dr. Martin Redmann, Martin-Luther-Universität Halle-Wittenberg:
Solving high-dimensional optimal stopping problems using model order reduction (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
Solving optimal stopping problems by backward induction in high dimensions is often very complex since the computation of conditional expectations is required. Typically, such computations are based on regression, a method that suffers from the curse of dimensionality. Therefore, the objective of this presentation is to establish dimension reduction schemes for large-scale asset price models and to solve related optimal stopping problems (e.g. Bermudan option pricing) in the reduced setting, where regression is feasible. We illustrate the benefit of our approach in several numerical experiments, in which Bermudan option prices are determined.

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Wednesday, 27.04.2022, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Michael Kniely, Universität Graz, Österreich:
From energy- to electro-energy-reaction-diffusion systems (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
This talk will be concerned with a thermodynamically correct formulation of reaction-diffusion systems describing the dynamics of charged species. This is achieved by employing the Onsager formalism of gradient flow systems along with Poisson's equation for the electrostatic potential. In the first part of the talk, we shall revisit some fundamental works on the thermodynamical modeling of semiconductor-type equations, while special emphasis will be placed on recent results on energy-reaction-diffusion systems. The second part will focus on electro-energy-reaction-diffusion models, in particular, the choice of appropriate entropies, the dependence of the Onsager operator on the electrostatic potential, and the existence of fundamental conservation laws. Finally, I will also comment on the expected outcome of the project concerning the well-posedness and the long-time asymptotics of our electro-energy-reaction-diffusion models. Proving the corresponding results is still work to be done and one of the goals of my two-year stay at WIAS.

Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 27.04.2022, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Dr. Nazgul Zakiyeva, Zuse-Institut Berlin/National University of Singapore:
Modeling and forecasting the dynamics of the natural gas transmission network in Germany with the demand and supply balance constraint (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We develop a novel large-scale Network Autoregressive model with balance Constraint (NAC) to predict hour-ahead gas flows in the gas transmission network, where the total in- and out-flows of the network are balanced over time. By integrating recent advances in optimization and statistical modeling, the NAC model can provide an accurate hour-ahead forecast of the gas flow at all of the distribution points in the network. By detecting the influential nodes of the dynamic network, taking into account that demand and supply have to be balanced, the forecast can be used to compute an optimized schdule and resource allocation. We demonstrate an application of our model in forecasting hour-ahead gas in- and out-flows at 128 nodes in the German high-pressure natural gas transmission network over a time frame of 22 months. Link to the paper: https://www.sciencedirect.com/science/article/abs/pii/S0306261920311

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 26.04.2022, 13:30 (Online Event)
Seminar Materialmodellierung
Ass. Prof. Dr. Alessia Nota, Università degli Studi dell'Aquila, Italien:
Stationary non-equilibrium solutions for coagulation equations (online talk)
more ... Location
Online Event

Abstract
Smoluchowski's coagulation equation, an integro-differential equation of kinetic type, is a classical model for mass aggregation phenomena extensively used in the analysis of problems of polymerization, particle aggregation in aerosols, drop formation in rain and several other situations. In this talk I will present some recent results on the problem of existence or non-existence of stationary solutions to coagulation equations, for single and multi-component systems, under non-equilibrium conditions which are induced by the addition of a source term for small cluster sizes. The most striking feature of these stationary solutions is that, whenever they exist, the solutions to multi-component systems exhibit an unusual “spontaneous localization” phenomena. More precisely, the stationary solutions to the multi-component coagulation equation asymptotically localize into a direction determined by the source term. The localization is a universal property of these multicomponent systems. Indeed, it has been recently proved that localization phenomenon occurs with a great degree of generality also for time dependent solutions to mass conserving coagulation equations. (Joint work with M.A. Ferreira, J. Lukkarinen and J.J.L. Velázquez)

Host
WIAS Berlin
Friday, 22.04.2022, 13:00 (Online Event)
E-Coffee-Lecture
Dr Renita Danabalan, WIAS:
Project Management Tools: Hype or Hack
more ... Location
Online Event

Host
WIAS Berlin
Wednesday, 20.04.2022, 12:30 (WIAS-405-406)
Seminar Interacting Random Systems
Martin Heida, WIAS Berlin:
Measure theoretic aspects of stochastic homogenization
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
We introduce stochastic homogenization of discrete and continuous differential operators as a measure theoretic concept. We then provide several examples for application to real-world problems.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Wednesday, 20.04.2022, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. Dr. Wolfgang Karl Härdle, BRC Blockchain Research Center:
DAI the digital art index (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
The DAI Digital Art index has been developed to reflect the increasing activities on the the Digital Art market. Based on the most liquid exchanges, NFT data and prices are collected in cooperation with artnet.com, NYC . The NFT art market has risen sharply recently and is competing with traditional arts market. The observed transactions are analysed and an index is developed on a hedonic regression framework. We present an introduction into NFTs, explain their construction and "huberize" the hedonic regression context.

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 12.04.2022, 16:00 (Online Event)
Seminar Weierstrass Group Data-Driven Optimization and Control
Adam Thorpe, University of New Mexico, USA:
Stochastic optimal control & safety via kernel embeddings: A data-driven approach
more ... Location
Online Event

Abstract
As autonomy becomes more prevalent, it is increasingly being deployed in highly uncertain environments. This motivates the need for data-driven control methods which are capable of handling complex systems, humans in the loop, poorly-structured disturbances, and also provide assurances of safety. We present a computationally efficient approach for computing stochastic policies based in the theory of kernel embeddings of distributions, a nonparametric statistical learning technique that embeds integral operators as elements in a high-dimensional function space known as a reproducing kernel Hilbert space. We demonstrate how this representation enables us to compute stochastic policies as a linear program, and enables tractability for a wide variety of systems which are resistant to traditional modeling techniques. We have implemented these techniques in a publicly-available toolbox, and apply our approach to motion planning problems and demonstrate its use for computing the safety probabilities for stochastic reachability problems.
Zoom link:
https://us02web.zoom.us/j/83039302328?pwd=S1IyTnBEZ3hDcmdNNmExallxVGp4UT09
Meeting ID: 830 3930 2328
Passcode: 596204

Host
WIAS Berlin
April 11 – 14, 2022 (Harnack-Haus)
Workshop/Konferenz: First Annual Conference of SPP 2265 Random Geometric Systems
more ... Location
Harnack-Haus -- Tagungsstätte der Max-Planck-Gesellschaft

Host
DFG Schwerpunktprogramm 2265
WIAS Berlin
Wednesday, 06.04.2022, 12:30 (WIAS-ESH)
Seminar Interacting Random Systems
Simone Baldassarri, University of Florence, Italien:
Critical Droplets and sharp asymptotics for Kawasaki dynamics with strongly anisotropic interactions
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In this talk we analyze metastability and nucleation in the context of the Kawasaki dynamics for the two-dimensional Ising lattice gas at very low temperature. Particles perform simple exclusion on a finite box in the bidimensional lattice, but when they occupy neighboring sites they feel a binding energy -U_1<0 in the horizontal direction and -U_2<0 in the vertical one. We consider the parameter regime U_1>2U_2 also known as the strongly anisotropic regime. For this model the empty (respectively full) configuration is a metastable (respectively stable) configuration. We consider the asymptotic regime corresponding to finite volume in the limit as the temperature goes to zero. We investigate how the transition from empty to full takes place with particular attention to the critical configurations that asymptotically have to be crossed with probability 1. To this end, we provide a model-independent strategy to identify some unessential saddles (that are not in the union of minimal gates) for the transition from the metastable (or stable) to the stable states and we apply this method to our model. The derivation of some geometrical properties of the saddles allows us to identify the full geometry of the minimal gates and their boundaries for the nucleation in the strongly anisotropic case. We observe very different behaviors for this case with respect to the isotropic (U_1=U_2) and weakly anisotropic (U_1<2U_2) ones. Moreover, we derive sharp estimates for the asymptotic transition time for the strongly anisotropic case. This is based on a joint work with F. R. Nardi.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Thursday, 31.03.2022, 14:00 (WIAS-ESH)
Seminar Numerische Mathematik
Dr. Stefano Piani, International School for advance studies, Italien:
HDG methods for the Van Roosbroeck model
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In the early fifties of the twentieth century, Van Roosbroeck formulated the so-called fundamental semiconductor device equations: a system of three nonlinear coupled partial differential equations which describes potential distribution, carrier concentrations, and current flow in arbitrary semiconductor devices. In this model, charge carriers move because of two physical effects: diffusion and convection, with the latter often dominant. Performing a numerical simulation of the Van Roosbroeck equations represent a challenging problem, mainly because of their stiffness. A classical solution to this problem has been found in 1969 by Scharfetter and Gummel, who developed a nonstandard discretization method: a finite-volume scheme with a tailored numerical flux.
At the beginning of this century, instead, it has become more and more common to address convection-dominated problems using discontinuous Galerkin methods (DG methods). One of the main advantages of these methods is their ability to handle adaptive algorithms, working with meshes with hanging nodes and approximation of varying polynomial degrees. Unfortunately, when compared with the standard continuous finite elements, DG methods were often criticized for using too many globally coupled degrees of freedom.
During my talk, I will introduce a particular class of DG methods, the Hybridizable Discontinuous Galerkin Methods which exploit the classic techniques of static condensation to reduce the total number of globally coupled degrees of freedom and I will discuss the possibility of applying these methods to the Van Roosbroeck system, exploiting their similarities with the Scharfetter-Gummel scheme.

Further Informations
For zoom login details please contact ulrich.wilbrandt@wias-berlin.de.

Host
WIAS Berlin
Tuesday, 29.03.2022, 15:00 (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. William Salkeld, WIAS Berlin:
Lions calculs and mean-field elementary differentials (online talk)
more ... Location
Online Event

Abstract
This talk will explore higher order Lions derivatives and provide some applications to the modelling of mean-field dynamic systems.

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Friday, 25.03.2022, 13:00 (Online Event)
E-Coffee-Lecture
Dr. Karsten Tabelow/Dr. Thomas Koprucki, WIAS:
HackMD
more ... Location
Online Event

Abstract
Collaborative online markdown editor

Host
WIAS Berlin
Thursday, 24.03.2022, 14:00 (WIAS-ESH)
Seminar Numerische Mathematik
Dr. Nicola Courtier, University of Oxford, UK:
Part I: Accurate and adaptable charge transport modelling of perovskite solar cells using IonMonger (hybrid talk)
Part II: Parameter/state estimation using the measure-moment approach to polynomial optimisation (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
This talk will cover the two main foci of my work to-date on the simulation of perovskite solar cell and lithium-ion battery models. Firstly, the development of a fast and accurate finite element scheme for a one-dimensional drift-diffusion model of a perovskite solar cell. This scheme underpins the open-source Matlab code IonMonger released in 2019 [1]. The latest version simulates a 100-point impedance spectroscopy measurement in less than a minute on a desktop computer. The ability of the scheme to cope with nonlinear terms, while maintaining second-order local accuracy, enables it to be applied to a variety of similar models e.g. [2].
Secondly, we address the problem of global parameter estimation of the four parameters of a reduced-order model for the impedance spectra of a perovskite solar cell. The reduced model is derived via asymptotic analysis of the drift-diffusion model [3]. Parameter estimation is performed using a novel approach to polynomial optimisation based on advancements in the field of measure-moment theory, via the numerical solution of a sequence of semi-definite programs [4]. Though limited by the curse of dimensionality, the measure-moment approach may also be used for state estimation and optimal control of reduced-order models. We benchmark the method via application to battery models containing 2 or 4 states.

[1] N.E. Courtier, G. Richardson, and J.M. Foster. A fast and robust numerical scheme for solving models of charge carrier transport and ion vacancy motion in perovskite solar cells. Applied Mathematical Modelling, 63, 329348 (2018)
[2] I. Korotkin, S. Sahu, S. E. J. O'Kane, G. Richardson, and J. M. Foster. DandeLiion v1: An Extremely Fast Solver for the Newman Model of Lithium-Ion Battery (Dis)charge. Journal of The Electrochemical Society, 168, 060544 (2021)
[3] L. J. Bennett, A. J. Riquelme, N. E. Courtier, J. A. Anta, and G. Richardson. A new ideality factor for perovskite solar cells and an analytical theory for their impedance spectroscopy response. arXiv:2105.11226 (2021)
[4] D. Henrion, J.-B. Lasserre, and J. Löfberg. GloptiPoly 3: moments, optimization and semidefinite programming. Optimization Methods & Software, 24:4-5, 761-779 (2009)

Further Informations
For zoom login details please contact ulrich.wilbrandt@wias-berlin.de

Host
WIAS Berlin
Wednesday, 23.03.2022, 12:30 (WIAS-ESH)
Seminar Interacting Random Systems
Florian Nie, Technische Universität Berlin:
The stochastic F-KPP Equation and on/off branching coalescing Brownian Motion
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Seminar Interacting Random Systems (Online Event)

Host
WIAS Berlin
Thursday, 10.03.2022, 14:00 (WIAS-ESH)
Seminar Numerische Mathematik
Xu Li, Shandong University, China:
Two divergence-free reconstructions for Navier--Stokes simulations regarding EMA and robust estimates of kinetic energy error (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Navier--Stokes simulations with divergence-free elements have many fascinating properties such as EMA-conservation (EMA: kinetic energy, linear momentum and angular momentum), pressure-robustness and Re-semi-robustness. Due to the complexity of divergence-free elements, developing novel discretizations for the commonly used elements which possess similar properties is a very popular way in Navier-Stokes community. In this talk, we discuss two divergence-free reconstruction methods for Navier--Stokes simulations. The first method is obtained by replacing the advective velocity of the convective trilinear form with its a divergence-free approximation. The resulting method preserves kinetic energy and linear momentum under some appropriate senses. Regarding its error estimates, we prove that the Gronwall constant in the kinetic energy error bound does not depend on the inverse powers of viscosity explicitly, which is similar to the EMAC method. The second method is based on the pressure-robust reconstruction formulation in [A. Linke & C. Merdon, CMAME, 2016]. We propose a novel trilinear form which preserves (redefined) energy, momentum and angular momentum, while maintaining pressure-robustness. It can also be proven that the constants in the kinetic energy error bound do not depend on the inverse powers of viscosity explicitly, which is similar to the methods with divergence-free elements. In both methods we discuss the reconstruction operators in detail. Finally, we also show some numerical experiments with Taylor--Hood, MINI and Bernardi--Raugel elements, doing some comparisons with the EMAC method and some low order divergence-free element methods.
(This is a joint work with Hongxing Rui, Shandong University)

Further Informations
For zoom login details please contact ulrich.wilbrandt@wias-berlin.de

Host
WIAS Berlin
Wednesday, 09.03.2022, 12:30 (WIAS-ESH)
Seminar Interacting Random Systems
Alexander Hinsen, WIAS Berlin:
Chase-escape on a dynamic network
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We study a malware propagation model on top of a dynamic device-to-device network. Movement of devices is generated by a random waypoint model, restricted to a Poisson-Voronoi tessellation based street system. At time zero, malware infects a typical device. Infected devices infect adjacent susceptible devices. In order to detect and contain the spread, we introduce white knights: patched devices that detect infection attempts and retaliate by purging the infection and forcing an update. As white knights and susceptible devices don't interact, the countermeasure 'spreads' on the infection. We derive regimes for the survival of the malware in the presence of the white-knight counter measure and determine regimes in which the white-knights counter measure leads to a containment of the malware. This talk presents the results of a research agreement between WIAS and Orange SA.

Further Informations
Seminar Interacting Random Systems

Host
WIAS Berlin
Friday, 25.02.2022, 13:00 (Online Event)
E-Coffee-Lecture
Dr Pierre-Étienne Meunier:
Pijul distributed version control system
more ... Location
Online Event

Host

WIAS Berlin
Wednesday, 23.02.2022, 12:30 (WIAS-ESH)
Seminar Interacting Random Systems
Dr. Ana Djurdjevac, Zuse Institute Berlin:
Approximation of the Dean-Kawasaki equation
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Dean-Kawasaki equation describes the evolution of the density function of finitely many particles obeying Langevin dynamics. This equation is extremely singular (supercritical) due to its form and the low regularity of the noise. We will formulate a nonlinear SPDE approximation. First we will study the well-posedness of the approximated equation and its conservation properties. Furthermore, we will show the bound of the weak error. This is the joint work with H. Kremp and N. Perkowski.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Tuesday, 22.02.2022, 15:00 (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Pavel Dvurechensky, WIAS Berlin:
Hessian barrier algorithms for non-convex conic optimization (online talk)
more ... Location
Online Event

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Wednesday, 16.02.2022, 15:15 (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Petr Pelech, WIAS Berlin:
Penrose-Fife model with activated phase transformation - existence and effective model for slow-loading regimes (online talk)
more ... Location
Online Event

Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 16.02.2022, 10:00 (Online Event)
Forschungsseminar Mathematische Statistik
Prof. Céline Duval, Université de Paris:
Interacting Hawkes processes with multiplicative inhibition (online talk)
more ... Location
Online Event

Abstract
After a short introduction on Hawkes processes, we introduce a general class of mean-field interacting nonlinear Hawkes processes modelling the reciprocal interactions between two neuronal populations, one excitatory and one inhibitory. The model incorporates two features: inhibition, which acts as a multiplicative factor onto the intensity of the excitatory population and additive retroaction from the excitatory neurons onto the inhibitory ones. We detail the well-posedness of this interacting system as well as its dynamics in large population. The analysis of the longtime behavior of the mean-field limit process can be explicated. We illustrate numerically that inhibition and retroaction may be responsible for the emergence of limit cycles. (j.w. with E. Luçon and C. Pouzat)

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Thursday, 10.02.2022, 16:00 (Online Event)
Forschungsseminar Mathematische Modelle der Photonik
Shulin Wohlfeil, Ferdinand-Braun-Institut:
Experimental investigations of passively modelocked ridge-waveguide and tapered lasers emitting at 830 nm (online talk)
more ... Location
Online Event

Host
WIAS Berlin
Ferdinand-Braun-Institut, Leibniz-Institut für Höchstfrequenztechnik
Wednesday, 09.02.2022, 12:30 (WIAS-ESH)
Seminar Interacting Random Systems
Tobias Paul, HU Berlin:
Modelling interactions of mutation, dormancy and transfer
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Recently, a toy model for the interaction of mutation and horizontal transfer was proposed by Champagnat, Méléard and Tran (2021). We extend their model to include the effects of competition induced dormancy and recover the convergence of the logarithmic population sizes. While the result remains unchanged, the qualitative behaviour of the limiting functions may exhibit properties of the model without dormancy but also entirely new phenomena. As an example we can observe an interesting non-monotonicity in the success of the dormancy traits depending on the strength of the dormancy initiation probability. Furthermore, we will discuss possible extensions and generalizations of the model. (This is joint work with Jochen Blath and András Tóbiás, TU Berlin)

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Wednesday, 09.02.2022, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. Erwan Scornet, Ecole Polytechnique Paris, Frankreich:
Variable importance in random forests (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Nowadays, machine learning procedures are used in many fields with the notable exception of so-called sensitive areas (health, justice, defense, to name a few) in which the decisions to be taken are fraught with consequences. In these fields, it is necessary to obtain a precise decision but, to be effectively applied, these algorithms must provide an explanation of the mechanisms that lead to the decision and, in this sense, be interpretable. Unfortunately, the most accurate algorithms today are often the most complex. A classic technique to try to explain their predictions is to calculate indicators corresponding to the strength of the dependence between each input variable and the output to be predicted. In this talk, we will focus on variable importances designed for the original random forest algorithm: the Mean Decreased Impurity (MDI) and the Mean Decrease Accuracy (MDA). We will see how theoretical results provide guidance for their practical uses.

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 02.02.2022, 15:15 (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Upanshu Sharma, Freie Universität Berlin:
Variational structures beyond gradient flows (online talk)
more ... Location
Online Event

Abstract
Gradient flows is an important subclass of evolution equations, whose solution dissipates an energy 'as fast as possible'. This distinguishing feature endows these equations with a natural variational structure, which has received enormous attention over the last two decades. In recent years, it has become clear that if the gradient-flow equation originates from an underlying (reversible) stochastic particle system, then often the aforementioned variational structure is an exact decomposition of the large-deviation rate functional for the particle system. However, this decomposition and the corresponding gradient-flow structure breaks down if the underlying particles have additional non-dissipative effects (for instance in the case of non-reversible independent particles), even though the large-deviation rate functional is still available. Using the guiding example of independent non-reversible Markov jump particles, in this talk, I will discuss the various features of the rate functional and how it connects to relative entropy and Fisher information. Furthermore, I will show that if the underlying particle system is augmented with fluxes, then it is possible to derive gradient-flow-type structures in the non-reversible setting.

Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 02.02.2022, 12:30 (WIAS-ESH)
Seminar Interacting Random Systems
Dr. Quirin Vogel, NYU Shanghai, China, Volksrepublik:
Infinite loops - The limit of the Feynman representation of the Bose gas (online talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Around 75 years ago, Feynman used path-integration to represent a gas of (interacting) bosons in a finite volume by an ensemble of brownian bridges, aka loops. Bosons exhibit Bose--Einstein condensation - a state of matter in which a macroscopic proportion of the particles occupy the same quantum state. It has been conjectured that the condensate is represented by “infinite” loops. We “verify” this for several cases by proving that the finite volume representation converges to the superposition of finite loops and the random interlacements. Prior knowledge of bosons/mathematical physics is not required for this talk.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Wednesday, 02.02.2022, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. Alessandra Menafoglio, Politecnico Milano , Italien:
Object oriented data analysis in Bayes spaces: From distributional data to the analysis of complex shapes (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In the presence of increasingly massive and heterogeneous data, the statistical modeling of distributional observations plays a key role. Choosing the 'right' embedding space for these data is of paramount importance for their statistical processing, to account for their nature and inherent constraints. The Bayes space theory is a natural embedding space for (spatial) distributional data, and was successfully applied in varied settings. In this presentation, I will discuss the state-of-the-art methods for the modelling, analysis, and prediction of distributional data, with a particular attention to cases when their spatial dependence cannot be neglected. I will embrace the viewpoint of object-oriented spatial statistics (O2S2), a system of ideas for the analysis of complex data with spatial dependence. All the theoretical developments will be illustrated through their application on real data, highlighting the intrinsic challenges of a statistical analysis which follows the Bayes spaces approach. Applications will cover a varied range of fields, from the assessment of COVID-19 on mortality data to the analysis of complex shapes produced in additive manufacturing.

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 01.02.2022, 15:00 (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Alexandra Suvorikova, WIAS Berlin:
Robust k-means clustering in metric spaces (online talk)
more ... Location
Online Event

Abstract
In this work we investigate the theoretical properties of robust k-means clustering under assumption of adversarial data corruption. Namely, we provide non-asymptotic rates for excess distortion under weak model assumptions on the moments of the distribution.

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Wednesday, 26.01.2022, 15:15 (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Alexander Mielke, WIAS Berlin:
On two coupled degenerate parabolic equations motivated by thermodynamics (online talk)
more ... Location
Online Event

Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 26.01.2022, 10:00 (Online Event)
Forschungsseminar Mathematische Statistik
Prof. Pierre Jacob, ESSEC Business School, Frankreich:
Some methods based on couplings of Markov chain Monte Carlo algorithms (online talk)
more ... Location
Online Event

Abstract
Markov chain Monte Carlo algorithms are commonly used to approximate a variety of probability distributions, such as posterior distributions arising in Bayesian analysis. I will review the idea of coupling in the context of Markov chains, and how this idea not only leads to theoretical analyses of Markov chains but also to new Monte Carlo methods. In particular, the talk will describe how coupled Markov chains can be used to obtain 1) unbiased estimators of expectations and of normalizing constants, 2) non-asymptotic convergence diagnostics for Markov chains, and 3) unbiased estimators of the asymptotic variance of MCMC ergodic averages.

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Friday, 21.01.2022, 13:00 (WIAS-Library)
E-Coffee-Lecture
Dr. Matthias Liero, WIAS:
Coffee-Lecture: Automated building and testing of software projects using the WIAS Gitlab server
more ... Location
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411

Abstract
This talk gives an introduction to Gitlab pipelines on the recently installed Gitlab server at WIAS. We will discuss the basic ideas and concepts and go through a simple example of setting up such a pipeline.

Further Informations
The coffee-lecture will probably take place online

Host

WIAS Berlin
Wednesday, 19.01.2022, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. Dr. Denis Belomestny, Universität Duisburg-Essen:
Achieving optimal sample complexity in reinforcement learning via upper solutions (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 18.01.2022, 15:00 (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Yangwen Sun, Humboldt-Universität zu Berlin:
High dimensional change-point detection: A complete graph approach (online talk)
more ... Location
Online Event

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Wednesday, 12.01.2022, 15:15 (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Ass. Prof. Dr. Sebastian Schwarzacher, Charles University Prague, Tschechische Republik:
A variational approach to fluid-structure interactions (online talk)
more ... Location
Online Event

Abstract
In this talk some recent existence results in fluid-structure interactions are discussed. It focuses on the case when visco-elastic bulk solids are interacting with fluids. One of the characteristic difficulties of the respective PDE systems is the variable-in-time fluid domain being a part of the solution. The construction of solutions is by step-wise minimization. Such a variational approximation seems to be irreplaceable for large deformation solids, since the respective state spaces are (for physical reasons) non-convex. We introduce a two time-scale approximation scheme that is capable to construct second-order in time PDEs via step-wise minimization. Further it allows to construct weak solutions describing bulk solids interacting with fluids governed by the incompressible or compressible Navier-Stokes equations. The talk is based on collaborations with Benesova, Breit and Kampschulte.

Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 12.01.2022, 12:30 (WIAS-ESH)
Seminar Interacting Random Systems
Prof. Dr. Wolfgang König, WIAS Berlin:
The free energy of a box version of the interacting Bose gas Joint works with Adams and Collevecchio (2011) and with Collin and Jahnel (ongoing)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
The interacting quantum Bose gas is a random ensemble of many Brownian bridges (cycles) of various lengths with interactions between any pair of legs of the cycles. It is one of the standard mathematical models in which a proof for the famous Bose?Einstein condensation phase transition is sought for. We introduce a simplified version of the model in $mathbb Z^d$ instead of $mathbb R^d$ and with an organisation of the particles in deterministic boxes instead of Brownian cycles as the marks of a reference Poisson point process. We derive an explicit and interpretable variational formula in the thermodynamic limit for the canonical ensemble for any value of the particle density. In this formula, each of the microscopic particles and the macroscopic part of the configuration are seen explicitly (if they exist); the latter receives the interpretation of the condensate. The methods comprises a two step large-deviation approach for marked Poisson point processes and an explicit distinction into microscopic and macroscopic marks. We discuss the condensate phase transition in terms of existence of minimizer.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Wednesday, 12.01.2022, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Dr. Martin Wahl, Humboldt-Universität zu Berlin:
Functional estimation in log-concave location-scale families (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 11.01.2022, 10:15 (Online Event)
Seminar Nichtlineare Optimierung und Inverse Probleme
Dr. Feliks Nüske, Universität Paderborn:
Tensor-based methods for learning the Koopman semigroup (online talk)
more ... Location
Online Event

Further Informations
You can follow this talk by zoom: https://zoom.us/j/98493865627.

Host
WIAS Berlin
Wednesday, 05.01.2022, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Dr. Alexandra Suvorikova, WIAS Berlin:
Robust k-means in metric spaces and spaces of probability measures (online talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Friday, 17.12.2021, 13:00 (Online Event)
E-Coffee-Lecture
Dr. Silvia Polla, WIAS:
Research support services at the WIAS library
more ... Location
Online Event

Host
WIAS Berlin
Friday, 17.12.2021, 11:30 (Online Event)
Seminar Interacting Random Systems
Prof. Dr. Daniel Ueltschi, University of Warwick, GB:
Loop models and the universal distribution of the loop lengths (online talk)
more ... Location
Online Event

Abstract
I will review several models that consist of one-dimensional loops living in three-dimensional space. These models describe bosonic systems, and classical or quantum spin systems.. Their common feature is that the joint distribution of their loop lengths has universal behaviour: It is always a Poisson-Dirichlet distribution. Most of this theory is conjectural, but it is backed by numerical studies and some partial rigorous results.

Further Informations
Seminar Interactin Random Systems (Online Event) [attention: day of week changed]

Host
WIAS Berlin
Wednesday, 15.12.2021, 15:15 (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Jun.-Prof. Lara Trussardi, Universität Konstanz:
Two structure-preserving time discretizations for gradient flow. An application to GENERIC systems (online talk)
more ... Location
Online Event

Abstract
The equality between dissipation and energy drop is a structural property of gradient-flow dynamics. The classical implicit Euler scheme fails to reproduce this equality at the discrete level. We discuss two modifications of the Euler scheme satisfying an exact energy equality at the discrete level. Eventually, we address extensions to GENERIC flows and implement the case of the damped harmonic oscillator. This is based on a series of joint works with A. Jüngel and U. Stefanelli.

Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 14.12.2021, 15:00 (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Prof. Uli Sauerland/Dr. Anton Benz, Leibniz-Zentrum Allgemeine Sprachwissenschaft:
Numerical challenges in linguistic pragmatics (online talk)
more ... Location
Online Event

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Friday, 10.12.2021, 14:00 (Online Event)
MATH+ Thematic Einstein Semester on “Mathematics of Imaging in Real-World Challenges”
Prof. Dr. Bernhard Schmitzer, U Göttingen; Prof. Dr. G. Steidl, TU Berlin:
https://mathplus.de/topic-development-lab/tes-winter-2021-22/#tandemtalks
Christmas talk: Santa Claus needs optimal transport
more ... Location
Online Event

Abstract
Please find below the zoom details. No registration is required.
https://tu-berlin.zoom.us/j/69089092360?pwd=aklyWDJFcmwzSkdFRGtWSkorK3pvUT09 Passcode: 797448

Host
Humboldt-Universität zu Berlin
Technische Universität Berlin
WIAS Berlin
Wednesday, 08.12.2021, 15:15 (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Joachim Rehberg, WIAS Berlin:
Some new insights in second order divergence operators (online talk)
more ... Location
Online Event

Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 08.12.2021, 12:30 (Online Event)
Seminar Interacting Random Systems
Elena Magnanini, WIAS Berlin:
Limit theorems for the edge density in exponential random graphs (online talk)
more ... Location
Online Event

Abstract
In the present talk we focus on the derivation of some asymptotic properties for the family of exponential random graphs. This model can be seen as the generalization of the dense Erd?s-Rényi random graph and follows the statistical mechanics approach of defining a Hamiltonian to weight the probability measure on the space of graphs, assigning higher mass to graphs with ?desirable? properties. In particular our analysis will be focused on the edge-triangle model, a two-parameter family of exponential random graphs where the Hamiltonian only includes edge and triangle densities. We borrow tools from statistical mechanics together with large deviations techniques to obtain limit theorems for the edge density in the so-called replica symmetric regime, where the limiting free energy of the model is known together with a complete characterization of the phase diagram. First, we determine the asymptotic distribution of the edge density, as the graph size n tends to infinity, in the entire replica symmetric regime. In particular, we obtain a strong law of large numbers when the parameters are chosen outside the critical curve and the convergence to a mixture of Dirac measures whenever working on the critical curve. We then study the fluctuations of the edge density around its average for all parameter values outside the critical curve and off the critical point and we formulate conjectures about the behavior at criticality based on the analysis of a mean-field approximation of the model. Joint work with Alessandra Bianchi and Francesca Collet.

Further Informations
Seminar Interacting Random Systems (Online Event)

Host
WIAS Berlin
Wednesday, 08.12.2021, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. Davy Paindaveine, Université Libre de Bruxelles, Belgien:
Hypothesis testing on high-dimensional spheres: The Le Cam approach (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Hypothesis testing in high dimensions has been a most active research topics in the last decade. Both theoretical and practical considerations make it natural to restrict to sign tests, that is, to tests that uses observations only through their directions from a given center. This obviously maps the original Euclidean problem to a spherical one, still in high dimensions. With this motivation in mind, we tackle two testing problems on high-dimensional spheres, both under a symmetry assumption that specifies that the distribution at hand is invariant under rotations with respect to a given axis. More precisely, we consider the problem of testing the null hypothesis of uniformity ("detecting the signal") and the problem of testing the null hypothesis that the symmetry axis coincides with a given direction ("learning the signal direction"). We solve both problems by exploiting Le Cam's asymptotic theory of statistical experiments, in a double- or triple-asymptotic framework. Interestingly, contiguity rates depend in a subtle way on how well the parameters involved are identified as well as on a possible further antipodally-symmetric nature of the distribution. In many cases, strong optimality results are obtained from local asymptotic normality. When this cannot be achieved, it is still possible to establish minimax rate optimality.

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 07.12.2021, 15:00 (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Oleg Butkovsky, WIAS Berlin:
Inverting the Markovian projection: A reproducing kernel Hilbert space approach (online talk)
more ... Location
Online Event

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Tuesday, 07.12.2021, 10:15 (Online Event)
Seminar Nichtlineare Optimierung und Inverse Probleme
André Eikmeier, Technische Universität Berlin:
Existence of weak solutions to a general multivalued differential equation (online talk)
more ... Location
Online Event

Further Informations
You can follow this talk by zoom: https://zoom.us/j/98493865627.

Host
WIAS Berlin
Monday, 06.12.2021, 15:00 (Online Event)
Berlin Oberseminar: Optimization, Control and Inverse Problems
Prof. Dr. Juan Carlos de los Reyes, Escuela Politécnica Nacional, Ecuador:
Bilevel learning for inverse problems
more ... Location
Online Event

Abstract
In recent years, novel optimization ideas have been applied to several inverse problems in combination with machine learning approaches, to improve the inversion by optimally choosing different quantities/functions of interest. A fruitful approach in this sense is bilevel optimization, where the inverse problems are considered as lower-level constraints, while on the upper-level a loss function based on a training set is used. When confronted with inverse problems with nonsmooth regularizers or nonlinear operators, however, the bilevel optimization problem structure becomes quite involved to be analyzed, as classical nonlinear or bilevel programming results cannot be directly utilized. In this talk, I will discuss on the different challenges that these problems pose, and provide some analytical results as well as a numerical solution strategy. Access to seminar over Zoom link on page https://www.wias-berlin.de/research/rgs/fg8/Seminar_Opt_Con_Inv_Prob/index.jsp?lang=1

Further Informations
Berlin Oberseminar: Optimization, Control and Inverse Problems

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 01.12.2021, 15:15 (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Lukas Wessels, Technische Universität Berlin:
Pontryagin's maximum principle for SPDEs and its relation to dynamic programming (online talk)
more ... Location
Online Event

Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 01.12.2021, 10:00 (Online Event)
Forschungsseminar Mathematische Statistik
Nikita Puchkin, Higher School of Economics Moscow, Russische Föderation:
Rates of convergence for density estimation with GANs (online talk)
more ... Location
Online Event

Abstract
We undertake a thorough study of the non-asymptotic properties of the vanilla generative adversarial networks (GANs). We derive theoretical guarantees for the density estimation with GANs under a proper choice of the deep neural networks classes representing generators and discriminators. In particular, we prove that the resulting estimate converges to the true density p* in terms of Jensen-Shannon (JS) divergence at the rate (logn/n)2β/(2β+d) where n is the sample size and β determines the smoothness of p*. Moreover, we show that the obtained rate is minimax optimal (up to logarithmic factors) for the considered class of densities.

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 30.11.2021, 15:00 (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Long-Hao Xu, University of Manchester:
Limiting behavior of the gap between the largest two representative points of statistical distributions (online talk)
more ... Location
Online Event

Abstract
The problem of selecting a given number of representative points retaining as much information as possible arises in many situations. It can also be considered as a problem of approximating a continuous distribution by a discrete distribution. In this talk, we are interested in these points reaching the minimum value of mean squared error (we call these points MSE RPs). We illustrate the relationship between MSE RPs and doubly truncated mean residual life (DMRL) as well as mean residual life (MRL), and we discuss the limiting behavior of the gap between the largest two MSE RPs. In simulation studies, we assess the statistical performance of MSE RPs for various distributions in terms of moment estimation and resampling technique. We also discuss the relationship between the tail of the distribution and the gap of MSE RPs.

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Tuesday, 30.11.2021, 10:15 (Online Event)
Seminar Nichtlineare Optimierung und Inverse Probleme
Paul Hagemann, Technische Universität Berlin:
Stochastic normalizing flows and inverse problems (online talk)
more ... Location
Online Event

Further Informations
You can follow this talk by zoom: https://zoom.us/j/98493865627.

Host
WIAS Berlin
Wednesday, 24.11.2021, 15:15 (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Tomáš Roubíček, Czech Academy of Sciences, Tschechische Republik:
Visco-plastic elastodynamics at large deformations by Eulerian approaches (online talk)
more ... Location
Online Event

Abstract
Two models of hardening-free plasticity or creep at large deformations will be presented in an Eulerian rate formulation based on two standard concepts, Green--Naghdi additive decomposition and Kroner--Lee--Liu multiplicative decomposition of the total strain. Extensions towards poroelasticity and thermodynamics will be outlined, too.

Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 24.11.2021, 14:00 (Online Event)
Forschungsseminar Mathematische Statistik
Prof. Matthew Reimherr, Penn State University:
Pure differential privacy in functional data analysis (online talk)
more ... Location
Online Event

Abstract
We consider the problem of achieving pure differential privacy in the context of functional data analysis, or more general nonparametric statistics, where the summary of interest can naturally be viewed as an element of a function space. In this talk I will give a brief overview and motivation for differential privacy before delving into the challenges that arise in the sanitization of an infinite dimensional summary. I will present a new mechanism, called the Independent Component Laplace Process, for achieving privacy followed by several applications and examples.

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 24.11.2021, 11:30 (Online Event)
Seminar Interacting Random Systems
Sanjoy Kumar Jhawar, WIAS Berlin:
Percolation in enhanced random connection models (online talk)
more ... Location
Online Event

Abstract
This work contains the study of phase transition and percolation at criticality for three random graph models on the plane, viz., the homogeneous and inhomogeneous enhanced random connection models (RCM) and the Poisson stick model. These models are built on a homogeneous Poisson point process P(s) with intensity parameter s, on the 2-d plane. In the homogeneous RCM, the vertices at x and y are connected with probability, which is a function of distance between the points, independent of everything else. In the inhomogeneous version of the model, points of P(s) are endowed with weights that are non-negative independent random variables W, having power law distribution. Vertices located at x, y with weights W(x), W(y) are connected with probability, that is a connection function depending on the distance between x, y and the weights attached to them, independent of all else. The edges of the graph are viewed as straight line segments starting and ending at points of P(s). The Poisson stick model consists of line segments of independent random lengths and orientation with the midpoint of each line located at a distinct point of P(s). Intersecting line segments form a path in the graph. In other words, a path in these graphs is a continuous curve that is a subset of the collection of all these line segments. A graph is said to percolate if there is an infinite connected component or path. The conditions for the existence of non-trivial phase transition has been derived. Under some additional conditions it has been shown that there is no percolation at criticality using Russo--Seymour-Welsh theory as a fundamental tool.

Host
WIAS Berlin
Tuesday, 23.11.2021, 13:30 (Online Event)
Seminar Materialmodellierung
Dr.-Ing. Silvia Budday, Friedrich-Alexander Universität Erlangen-Nürnberg:
Brain mechanics across scales (online talk)
more ... Location
Online Event

Further Informations
Seminar Materialmodellierung

Host
WIAS Berlin
Tuesday, 23.11.2021, 10:15 (Online Event)
Seminar Nichtlineare Optimierung und Inverse Probleme
Dr. Jia-Jie Zhu, WIAS Berlin:
Numerical, statistical, and functional analysis of robust optimization-learning-control
more ... Location
Online Event

Abstract
In this talk, I will first introduce our works in establishing computational algorithms for robust learning and optimization algorithms, highlighting the use of kernel methods and optimal transport in treating the ubiquitous data distribution shift that plagues modern-day machine learning. I will do so by presenting perspectives from numerical optimization and optimal control, statistical learning theory, function spaces and approximations. In the latter half, the talk will focus on the outlook on multi-stage problems and topics beyond the classical notion of robustness, highlighting technical limitations, what we already know, and what we do not yet know.

Further Informations
You can follow this talk by zoom: https://zoom.us/j/98493865627.

Host
WIAS Berlin
Thursday, 18.11.2021, 16:00 (Online Event)
Forschungsseminar Mathematische Modelle der Photonik
Lasse Ermoneit, WIAS Berlin:
Multi-physics device-scale modeling for solid-state spin-qubits (online talk)
more ... Location
Online Event

Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://us02web.zoom.us/j/83433220391?pwd=UzNsUktDSTR3K0tkOU1KNTRSRjFBdz09

Host
WIAS Berlin
Humboldt-Universität zu Berlin
Thursday, 18.11.2021, 14:00 (WIAS-ESH)
Seminar Numerische Mathematik
Dr. Felipe Galarce Marín, WIAS Berlin:
Physics-based assimilation of displacements data from magnetic resonance elastography (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
This work addresses the state estimation problem of reconstructing 3D displacement fields from partial 2D data acquired with Magnetic Resonance Elastography (MRE). MRE is a medical imaging technique sensitive to mechanical properties of tissues. Recent studies demonstrated its potential for the non-invasive estimation of pathological interstitial pressure, e.g., in the contexts of hydrocephalus (brain). We use a variational data assimilation framework based on a background parametric PDE (poroelasticity) for the tissue dynamics and on model order reduction (POD) of the admissible solution space. Preliminary results for the reconstruction of displacement field and characterization of the pressure field are presented.
For zoom login details please contact Ulrich Wilbrandt wilbrandt@wias-berlin.de

Host
WIAS Berlin
Wednesday, 17.11.2021, 15:15 (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. André Schlichting, Westfälische Wilhelms-Universität Münster:
Dynamic behavior of growth processes: Phase separation, self-similarity, and oscillations (online talk)
more ... Location
Online Event

Abstract
The talk reviews some growth processes describing the evolution of clusters consisting of atomic parts called monomers. The growth and shrinkage can only occur by adding and removing single monomers, specified through a rate kernel depending solely on the involved clusters' size. First, I discuss the exchange-driven growth model, obtained as the mean-field limit of stochastic particle systems (zero-range process). Under a detailed balance condition on the kernel, the model's longtime behavior can be described entirely. Here, the total mass density, determined by the initial data, acts as an order parameter in which the system shows a phase separation. Next, we consider the model for a family of product kernels, which do not satisfy a detailed balance condition. After a suitable rescaling to self-similar variables, the equation becomes a discrete Laplace with a power-law as diffusion coefficient, which in particular degenerates at the origin and grows at infinity. We will see that the solution converges to a stretched exponential self-similar profile. Lastly, we consider the now-classic Becker-Döring system to which an injection of monomers and a depletion of large clusters is added. These equations have been extensively used to model chemical-physical systems, especially bubbleator dynamics. The model approximates a transport equation with a conservation law entering the boundary condition by formal asymptotics. For the limit model, a Hopf bifurcation is shown, indicating temporal oscillations in the model. joint works with Constantin Eichenberg, Barbara Niethammer, Robert Pego, and Juan Velazquez.

Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 17.11.2021, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. Christophe Giraud, Université Paris-Saclay, Frankreich:
A geometric approach to fair online learning (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Machine learning is ubiquitous in daily decisions and producing fair and non-discriminatory predictions is a major societal concern. Various criteria of fairness have been proposed in the literature, and we will start with a (biased!) tour on fairness concepts in machine learning. Many decision problems are of a sequential nature, and efforts are needed to better handle such settings. We consider a general setting of fair online learning with stochastic sensitive and non-sensitive contexts. We propose a unified approach for fair learning in this setting, by interpreting this problem as an approachability problem. This point of view offers a generic way to produce algorithms and theoretical results. Adapting Blackwell?s approachability theory, we exhibit a general necessary and sufficient condition for some learning objectives to be compatible with some fairness constraints, and we characterize the optimal trade-off between the two, when they are not compatible. (joint work with E. Chzhen and G. Stoltz)

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Friday, 12.11.2021, 15:00 (Online Event)
MATH+ Thematic Einstein Semester on “Mathematics of Imaging in Real-World Challenges”
Prof. Dr. Tobias Schäffter, TU Berlin and PTB; Prof. Dr. Michael Hintermüller, WIAS and HU Berlin:
Tandem Talk: Quantitative Magnetic Resonance Imaging: Applications and Mathematics (online talks):

Tobias Schäffter (TU Berlin, PTB): Quantitative MR Imaging -- Added Value
Michael Hintermüller (WIAS, HU Berlin): Mathematics of Quantitative Imaging
https://mathplus.de/topic-development-lab/tes-winter-2021-22/#tandemtalks
more ... Location
Online Event

Abstract
Please find below the zoom details. No registration is required.
Topic: TES Tandem Talk: qMRI - Applications and Mathematics
Time: Nov 12, 2021 15:00 Amsterdam, Berlin, Rome, Stockholm, Vienna
Join Zoom Meeting
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Meeting ID: 684 2394 2351
Passcode: 359737
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Meeting ID: 684 2394 2351
Passcode: 359737


Host
Humboldt-Universität zu Berlin
Technische Universität Berlin
WIAS Berlin
Thursday, 11.11.2021, 16:00 (WIAS-ESH)
Forschungsseminar Mathematische Modelle der Photonik
Dr. Mindaugas Radziunas, WIAS Berlin:
Steady states in the Traveling Wave model of multisection edge emitting semiconductor lasers (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Diesen Vortrag können Sie auch mit Zoom verfolgen unter: https://us02web.zoom.us/j/83433220391?pwd=UzNsUktDSTR3K0tkOU1KNTRSRjFBdz09

Host
WIAS Berlin
Humboldt-Universität zu Berlin
Wednesday, 10.11.2021, 15:15 (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Petr Vágner, WIAS Berlin:
GENERIC, geometry and continuum electro-thermodynamics (online talk)
more ... Location
Online Event

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 10.11.2021, 14:00 (HU)
Forschungsseminar Mathematische Statistik
Nikita Zhivotovsky, Google Research:
Distribution--free robust linear regression
more ... Location
Humboldt-Universität zu Berlin, Dorotheenstr. 1, 10117 Berlin, Raum 005

Abstract
We study random design linear regression with no assumptions on the distribution of the covariates and with a heavy--tailed response variable. When learning without assumptions on the covariates, we establish boundedness of the conditional second moment of the response variable as a necessary and sufficient condition for achieving deviation-optimal excess risk bounds. First, we prove an optimal version of the classical in-expectation bound for the truncated least squares estimator due to Györfi, Kohler, Krzyzak, and Walk. However, in spite of its optimal in--expectation performance, we show that this procedure fails with constant probability for some distributions. Combining the ideas of truncated least squares, median-- of--means procedures, and aggregation theory, we construct a non--linear estimator achieving excess risk of order O(d/n) with the optimal sub-exponential tail. Joint work with Jaouad Mourtada (CREST, ENSAE) and Tomas Vaškevičius (University of Oxford)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 10.11.2021, 11:30 (Online Event)
Seminar Interacting Random Systems
Anh Duc Vu, WIAS Berlin:
Percolation theory and effective conductivity (online talk)
more ... Location
Online Event

Abstract
Percolation theory is getting more and more attention in recent years and we have already seen applications in previous IRS talks, e.g. in the modelling of device-to-device networks. The motivation for this talk lies in a different field, namely PDEs on randomly perforated domains. This field is highly driven by the analysis of composite materials. We derive a formula for the so-called "effective conductivity" of an ergodic random perforation. While there are many ways to calculate the effective conductivity in an analytic way, this formula uses percolation properties of the random perforation to derive its value. As a direct application, we show that the Boolean model of a Poisson point process has non-trivial effective conductivity.

Host
WIAS Berlin
Wednesday, 10.11.2021, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. Marc Hoffmann, Université Paris-Dauphine:
Some statistical inference results for interacting particle models in a mean-field limit (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We propose a systematic--theoretical--statistical analysis for systems of interacting diffusions, possibly with common noise and/or degenerate diffusion components, in a mean-field regime. These models are more or less widely used in finance, MFG, systemic risk analysis, behaviourial sociology or ecology. We consider several inference issues such as: i) nonparametric estimation of the solution of the underlying Fokker-Planck type equation or the drift of the system ii) testing for the interaction between components iii) estimation of the interaction range between particles. This talk is based on joint results with C. Fonte, L. Della Maestra and R. Maillet.

Further Informations
Der Vortrag findet auch bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 09.11.2021, 15:00 (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Simon Breneis, WIAS Berlin:
Markovian approximations of stochastic Volterra equations with the fractional kernel (online talk)
more ... Location
Online Event

Abstract
We consider rough stochastic volatility models where the variance process satisfies a stochastic Volterra equation with the fractional kernel, as in the rough Bergomi and the rough Heston model. In particular, the variance process is therefore not a Markov process or semimartingale, and has quite low Hölder-regularity. In practice, simulating such rough processes thus often results in high computational cost. To remedy this, we study approximations of stochastic Volterra equations using an $N$-dimensional diffusion process defined as solution to a system of ordinary stochastic differential equation. If the coefficients of the stochastic Volterra equation are Lipschitz continuous, we show that these approximations converge strongly with superpolynomial rate in $N$. Finally, we apply this approximation to compute the implied volatility smile of a European call option under the rough Bergomi and the rough Heston model.

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Wednesday, 03.11.2021, 10:00 (Online Event)
Forschungsseminar Mathematische Statistik
Prof. Evgeny Stepanov, Russian Academy of Sciences, Russische Föderation:
The story of a fish in a turbulent ocean: How to survive and how to return home
more ... Location
Online Event

Abstract
Can a fish with limited velocity capabilities reach any point in the (possibly unbounded) ocean? In a recent paper by D. Burago, S. Ivanov and A. Novikov, “A survival guide for feeble fish", an affirmative answer has been given under the condition that the fluid velocity field is incompressible, bounded and has vanishing mean drift. This brilliant result extends some known point-to-point global controllability theorems though being substantially non constructive. We will give a fish a different recipe of how to survive in a turbulent ocean, and show how this is related to structural stability of dynamical systems by providing a constructive way to change slightly a divergence free vector field with vanishing mean drift to produce a non dissipative dynamics. This immediately leads to closing lemmas for dynamical systems, in particular to C. Pugh's closing lemma, saying also that the fish can eventually return home. Joint work with Sergey Kryzhevich (St. Petersburg).

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 02.11.2021, 15:15 (Online Event)
Oberseminar Nonlinear Dynamics
Prof. Jaroslav Hlinka, Institute of Computer Science of the Czech Academy of Sciences:
Perturbations both trigger and delay seizures due to generic properties of slow--fast relaxation oscillators (online talk)
more ... Location
Online Event

Abstract
The mechanisms underlying the emergence of seizures are one of the most important unresolved issues in epilepsy research. In this work, we analyze white and how perturbations, exogenous or endogenous, may promote or delay seizure emergence [1], following previous observations in vivo, in vitro and in silico [2]. To this aim, due to the increasingly adopted view of epileptic dynamics in terms of slow-fast systems, we perform a theoretical analysis of the phase response of a generic relaxation oscillator. As relaxation oscillators are effectively bistable systems at the fast time scale, it is intuitive that perturbations of the non-seizing state with a suitable direction and amplitude may cause an immediate transition to seizure. By contrast, and perhaps less intuitively, smaller amplitude perturbations have been found to delay the spontaneous seizure initiation. By studying the isochrons of relaxation oscillators, we show that this is a generic phenomenon, with the size of such delay depending on the slow flow component. Therefore, depending on perturbation amplitudes, frequency and timing, a train of perturbations causes an occurrence increase, decrease or complete suppression of seizures. This dependence lends itself to analysis and mechanistic understanding through methods outlined in this paper. We illustrate this methodology by computing the isochrons, phase response curves and the response to perturbations in several epileptic models possessing different slow vector fields. While our theoretical results are applicable to any planar relaxation oscillator, in the motivating context of epilepsy they elucidate mechanisms of triggering and abating seizures, thus suggesting stimulation strategies with effects ranging from mere delaying to full suppression of seizures.

References
[1] Alberto Pérez-Cervera, Jaroslav Hlinka. Perturbations both trigger and delay seizures due to generic properties of slow-fast relaxation oscillators. PLOS Computational Biology, 17(3): e1008521, 2021.
[2] Chang, Wei-Chih, et al. "Loss of neuronal network resilience precedes seizures and determines the ictogenic nature of interictal synaptic perturbations." Nature neuroscience 21.12 (2018): 1742-1752.

Host
Freie Universität Berlin
WIAS Berlin
Wednesday, 27.10.2021, 15:15 (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Matthias Liero, WIAS Berlin:
Electrothermal drift-diffusion models for organic semiconductor devices (online talk)
more ... Location
Online Event

Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 27.10.2021, 11:30 (Online Event)
Seminar Interacting Random Systems
András Tóbiás, TU Berlin:
Virus dynamics in the presence of contact-mediated host dormancy (online talk)
more ... Location
Online Event

Abstract
Abstract: We investigate a stochastic individual-based model for the population dynamics of host-virus systems where the hosts may transition into a dormant state upon contact with virions, thus evading infection. Such a dormancy-based defence mechanism was described in Bautista et al (2015). We first analyse the effect of the dormancy-related model parameters on the probability of invasion of a newly arriving virus into a resident host population. It turns out that the probability of dormancy initiation upon virus contact plays a crucial role, while the lengths of the dormancy periods or the death rate during dormancy are largely irrelevant. Given successful invasion, we then show that the emergence of a persistent virus infection ('epidemic') in the host population corresponds to the existence of a coexistence equilibrium for the deterministic many-particle limit of our model. In this context, all dormancy-related parameters have a significant impact. Indeed, while related systems without recovery of infected individuals and dormancy may exhibit a Hopf bifurcation, giving rise to a variant of the 'paradox of enrichment', we provide simulations and rigorous partial results showing that the inclusion of dormancy and recovery can prevent this loss of stability. Finally, we show that the presence of contact-mediated dormancy enables the host population to maintain higher equilibrium sizes (resp. fitness values) - while still being able to avoid a persistent epidemic - than host populations without this trait, for which high fitness values would imply a high risk for the emergence of a persistent epidemic. This adds a twist to the relevance of 'reproductive trade-offs' usually associated with costly dormancy traits. The subject of this talk is joint work with Jochen Blath.

Further Informations
Seminar Interacting Random Systems (Online Event)

Host
WIAS Berlin
Wednesday, 20.10.2021, 15:15 (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Willem van Oosterhout, WIAS Berlin:
Longtime dynamics of a non-autonomous Chafee--Infante equation (online talk)
more ... Location
Online Event

Abstract
In this talk, we study the longtime dynamics of a one-dimensional Chafee--Infante equation, a particular type of reaction-diffusion equation. We start by giving a thorough description of the longtime dynamics of the autonomous equation. Then, we turn to a non-autonomous version of the Chafee--Infante equation, and see which autonomous results can be generalized to the nonautonomous case. To this end, we consider, for example, the notions of a pullback attractor and non-autonomous equilibria, which can be seen as generalizations of the autonomous concepts of a global attractor and equilibrium solutions.

Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 19.10.2021, 10:15 (Online Event)
Seminar Nichtlineare Optimierung und Inverse Probleme
Jan Hauffen, Technische Universität Berlin:
Deep unfolding: Learned block regularization with application in photothermal superresolution (online talk)
more ... Location
Online Event

Further Informations
You can follow this talk by zoom: https://zoom.us/j/98493865627.

Host
WIAS Berlin
Wednesday, 13.10.2021, 11:30 (Online Event)
Seminar Interacting Random Systems
Tejas Iyer, WIAS Berlin:
Degrees of fixed vertices and power law degree distributions in preferential attachment trees with neighbourhood influence (online talk)
more ... Location
Online Event

Abstract
Motivated by the structure of complex networks such as the internet, we consider a growing model of preferential attachment trees with neighbourhood influence, where vertices arrive one at a time, are equipped with independent weights, and connect to existing vertices with probability proportional to their fitness function: a function of their own weight and the weights of their neighbours. In this model we prove almost sure limiting statements for the proportion of vertices with a given degree having weight belonging to a given measurable set, and the proportion of edges in the tree with endpoint belonging to a measurable set. We show that under certain conditions, the latter quantity demonstrates a condensation phenomenon, in which a positive proportion of edges in the network accumulate among those of weight that confers maximal reinforcement of fitness. Finally, we derive almost sure limiting statements for the log of the degree of a fixed vertex in this model, and prove that in this model the degree distribution behaves like a power law - a ubiquitous feature of many real-world complex networks.

Further Informations
Seminar Interacting Random Systems (Online Event)

Host
WIAS Berlin
Wednesday, 29.09.2021, 11:30 (Online Event)
Seminar Interacting Random Systems
Michiel Renger, WIAS Berlin:
Open problem: large deviations of transport maps (online talk)
more ... Location
Online Event

Abstract
Motivated by nonequilibrium thermodynamics, we are interested in large deviations for transport maps as the number of particles n goes to infinity. We first focus on the simplest setting of independent Markovian particles on a finite state space, which already poses mathematical challenges. Let n Γ _xy(s,t) be the number of particles that were at position x at time s and at position y at time t. Common large-deviation techniques for random trajectories exploit the Markov property (in one time variable). However, Γ has two time dimensions; can we reformulate Γ as a Markov process?

Further Informations
Seminar Interacting Random Systems (Online Event)

Host
WIAS Berlin
Wednesday, 15.09.2021, 11:30 (Online Event)
Seminar Interacting Random Systems
Alexander Zass, WIAS Berlin:
Gibbs point processes on path space: existence, cluster expansion and uniqueness (online talk)
more ... Location
Online Event

Abstract
In this talk we present a class of infinite-dimensional diffusions under Gibbsian interactions, viewed in the context of marked point configurations: the starting points belong to R^d, and the marks are the paths of Langevin diffusions. We use the entropy method to prove existence of an infinite-volume Gibbs point process and use cluster expansion tools to provide an explicit activity domain in which uniqueness holds.

Further Informations
Seminar Interacting Random Systems (Online Event)

Host
WIAS Berlin
August 23 – 27, 2021 (Schloss Dagstuhl)
Workshop/Konferenz: Leibniz MMS Summer School 2021 “Mathematical Methods for Machine Learning”
more ... Location
Leibniz-Zentrum für Informatik, Schloss Dagstuhl

Abstract
Fundamental and advanced aspects of ML methods are presented with the aim to enable the participants to apply such methods to their specific research problems. The topics that will be discussed include kernel methods and Gaussian processes, stochastic and robust optimization, deep Neural Networks. In addition to daily lectures, the participants will get the opportunity to become familiar with the presented methods in accompanying practical lab sessions.

Host
WIAS Berlin
Tuesday, 17.08.2021, 15:00 (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Jia-Jie Zhu, WIAS Berlin/MPI-IS Tübingen:
Kernel methods for distributionally robust optimization and machine learning (online talk)
more ... Location
Online Event

Abstract
Learning under distribution shift brings new challenges that cannot be addressed by canonical statistical learning theory. In this talk, I will present the use of reproducing kernel Hilbert spaces (RKHS) as the dual spaces for enforcing distributional robustness in stochastic optimization and machine learning. I then prove a generalized strong duality for distributionally robust optimization (DRO) using the integral probability metrics (IPM), of which the type-1 Wasserstein metric is a special instance. Our analysis highlights the roles that smooth function majorants, such as RKHS functions and Moreau envelope, play in enforcing distributional robustness in optimization. Finally, I will introduce a new class of kernel semi-infinite programs that originated from the DRO reformulation.

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Tuesday, 10.08.2021, 15:00 (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Darina Dvinskikh, WIAS Berlin:
Decentralized algorithms for Wasserstein barycenters (online talk)
more ... Location
Online Event

Abstract
We consider the Wasserstein barycenter problem of discrete probability measures from computational and statistical sides in two scenarios: (i) the measures are given and we need to compute their Wasserstein barycenter, and (ii) the measures are generated from a probability distribution and we need to calculate the population barycenter of the distribution defined by the notion of Fréchet mean. The statistical focus is estimating the sample size of measures necessary to calculate an approximation for Fréchet mean (barycenter) of a probability distribution with a given precision. For empirical risk minimization approaches, the question of the regularization is also studied together with proposing a new regularization which contributes to the better complexity bounds in comparison with quadratic regularization. The computational focus is developing algorithms for calculating Wasserstein barycenters: both primal and dual algorithms which can be executed in a decentralized manner.

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Thursday, 15.07.2021, 14:00 (Online Event)
Seminar Numerische Mathematik
Prof. Marc-Andre Keip, Universität Stuttgart:
Multiscale analysis of instability-induced pattern transformations of composite active solids
more ... Location
Online Event

Abstract
We discuss instability phenomena of active solids with periodic microstructures. Depending on the material, instabilities can be triggered by different means. In a first part of the talk, we analyze instability-induced pattern transformations of electroactive polymer composites and magnetorheological elastomers. In a second part, we widen the view towards the transient analysis of diffusion-driven instabilities of hydrogels, where we study pattern transformations of composite hydrogel thin films at different length scales.
Acknowledgements: Elten Polukhov, Siddharth Sriram
References
[1] G. Geymonat, S. Müller and N. Triantafyllidis. Homogenization of nonlinearly elastic materials, microscopic bifurcation and macroscopic loss of rank-one convexity. Archive for Rational Mechanics and Analysis 122:231-290 (1993)
[2] K. Bertoldi, M. Boyce, S. Deschanel, S. Prange and T. Mullin. Mechanics of deformation-triggered pattern transformations and superelastic behavior in periodic elastomeric structures. Journal of the Mechanics and Physics of Solids 56:2642-2668 (2008)
[3] C. Tipton, E. Han and T. Mullin. Magneto-elastic buckling of a soft cellular solid. Soft Matter 8:6880-6883 (2012)
[4] Wu, G., Xia, Y., Yang, S. Buckling, symmetry breaking, and cavitation in periodically micro-structured hydrogel membranes. Soft Matter 10:1392-1399 (2014)
[5] Polukhov, E., Vallicotti, D. and Keip, M.-A. Computational stability analysis of periodic electroactive polymer composites across scales. Computer Methods in Applied Mechanics and Engineering 337:165-197 (2018)
[6] Polukhov, E. and Keip, M.-A. Multiscale stability analysis of periodic magnetorheological elastomers. Mechanics of Materials, 159:103699 (2021)
[7] Sriram, S., Polukhov, E. and Keip, M.-A. Transient stability analysis of composite hydrogel structures based on a minimization-type variational formulation. International Journal of Solids and Structures, 111080 (2021)

Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de

Host
WIAS Berlin
Wednesday, 14.07.2021, 15:15 (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Xin Liu, WIAS Berlin:
Well-posedness of Hibler's dynamical sea-ice model (online talk)
more ... Location
Online Event

Abstract
We establish the local-in-time well-posedness of solutions to an approximating system constrcuted by mildly regularizing the dynamical sea ice model of W.D. Hibler in 1979, which is widely used in the prediction of evolution of Artic sea ice. Our choice of regularization has been carefully designed, prompted by physical considerations, to retain the original coupled hyperbolic-parabolic character of Hibler's model. The well-posedness theory of such a system provides a first-step groundwork in both numerical study and future analytical study. This is joint work with Marita Thomas and Edriss Titi.

Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 13.07.2021, 15:15 (Online Event)
Oberseminar Nonlinear Dynamics
Prof. Dr. Messoud Efendiyev, Helmholtz Zentrum München:
Mathematical modeling of biofilms and their long-time dynamics (online talk)
more ... Location
Online Event

Abstract
In this talk we deal with mathematical modelling of biofilms, that show biofilm performance is non-uniform. Moreover, our model leads to a new class of degenerate PDEs. Effect of degeneracy to large time behavior of solutions will also be considered.

Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://us02web.zoom.us/j/84203723799?pwd=bmNVcVBaazRzSlI3TjAxV1U1S2xFQT09

Host
Freie Universität Berlin
WIAS Berlin
July 8, 2021 (Online Event)
Workshop/Konferenz: Minisymposium ”Perspectives of Gradient-Robustness”
more ... Location
Online Event

Host
WIAS Berlin
Wednesday, 07.07.2021, 15:15 (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Klaas Hendrik Poelstra, Technische Universität Dortmund:
Dimension reduction for elastoplastic rods and homogenization of elastoplastic lattices (online talk)
more ... Location
Online Event

Abstract
We derive effective equations for periodic lattices of linearly elastoplastic rods in the limit of both infinitesimal periodicity and infinitesimal relative width of the rods. For this derivation we use the method of evolutionary Gamma-convergence for quadratic rate-independent systems. As a first step towards that goal we derive effective equations for a single rod. After introducing appropriate scalings, the main difficulty lies in the proof of Gamma-convergence for the stored energy. For the study of periodic lattices we then introduce the notion of periodic graph frameworks, discuss infinitesimal rigidity properties of such frameworks and define a simple notion of two-scale convergence. The stored energy of a lattice of rods ist just the sum of the energies of the individual rods, coupled by boundary conditions at the nodes. For this energy we again prove Gamma-convergence. In the presence of volume loads we observe qualitatively different behaviour depending on the relative rate of convergence of the periodicity parameter and the thickness parameter.

Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 07.07.2021, 11:30 (Online Event)
Seminar Interacting Random Systems
Daoyi Wang, Leiden University:
The Parabolic Anderson Model on a Galton-Watson tree with unbounded degrees (online talk)
more ... Location
Online Event

Abstract
A detailed analysis was given by den Hollander, König and dos Santos (2020), of the large-time asymptotics of the total mass of the solution to the parabolic Anderson model on a supercritical Galton-Watson random tree, with an i.i.d. random potential whose marginal distribution is double-exponential. Under the assumption that the degree distribution has bounded support, two terms in the asymptotic expansion were identified under the quenched law, i.e., conditional on the realisation of the random tree and the random potential. We extend the analysis to degree distributions with unbounded support. We identify the weakest condition on the tail of the degree distribution under which the arguments can be pushed through. This is joint work with my supervisor Frank den Hollander.

Further Informations
Seminar Interacting Random Systems (Online Event)

Host
WIAS Berlin
Wednesday, 07.07.2021, 10:00 (Online Event)
Forschungsseminar Mathematische Statistik
Prof. Dr. Victor Panaretos, École Polytechnique Fédérale de Lausanne, Schweiz:
Testing for the rank of a covariance operator (online talk)
more ... Location
Online Event

Abstract
How can we discern whether the covariance operator of a stochastic process is of reduced rank, and if so, what its precise rank is? And how can we do so at a given level of con dence? This question is central to a great deal of methods for functional data, which require low-dimensional representations whether by functional PCA or other methods. The difficulty is that the determination is to be made on the basis of i.i.d. replications of the process observed discretely and with measurement error contamination. This adds a ridge to the empirical covariance, obfuscating the underlying dimension. We describe a matrix-completion inspired test statistic that circumvents this issue by measuring the best possible least square fit of the empirical covariance's off -diagonal elements, optimised over covariances of given nite rank. For a fixed grid of sufficiently large size, we determine the statistic's asymptotic null distribution as the number of replications grows. We then use it to construct a bootstrap implementation of a stepwise testing procedure controlling the family-wise error rate corresponding to the collection of hypotheses formalising the question at hand. Under minimal regularity assumptions we prove that the procedure is consistent and that its bootstrap implementation is valid. The procedure circumvents smoothing and associated smoothing parameters, is indi fferent to measurement error heteroskedasticity, and does not assume a low-noise regime. (Based on joint work with Anirvan Chakraborty.)

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 06.07.2021, 15:15 (Online Event)
Oberseminar Nonlinear Dynamics
Prof. Dr. Carsten Conradi, Hochschule für Technik und Wirtschaft Berlin:
Monomial parameterizations in the analysis of biochemical reaction networks (online talk)
more ... Location
Online Event

Abstract
The dynamics of biochemical reaction networks can be described by ODEs with polynomial right hand side. In this presentation networks are considered where the steady state variety can be parameterized by monomials. I present two applications of these monomial parameterizations in the analysis of reaction networks: (i) deciding multistationarity and (ii) establishing Hopf bifurcations. Here multistationarity refers to the existence of at least two positive solutions to the polynomial steady state equations. And if a monomial parameterization exists, then this question is equivalent to the feasibility of at least one linear inequality system (out of many). The results presented here can be used to determine parameter values where multistationarity or Hopf bifurcations occur.

Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://us02web.zoom.us/j/84203723799?pwd=bmNVcVBaazRzSlI3TjAxV1U1S2xFQT09

Host
Freie Universität Berlin
WIAS Berlin
Tuesday, 06.07.2021, 10:15 (Online Event)
Seminar Nichtlineare Optimierung und Inverse Probleme
Luisa Plato, WIAS Berlin:
Biological pest control -- Analysis and numerics for a spatio-temporal predator-prey system
more ... Location
Online Event

Further Informations
You can follow this talk by zoom: https://zoom.us/j/98493865627.

Host
WIAS Berlin
Monday, 05.07.2021, 15:00 (Online Event)
Berlin Oberseminar: Optimization, Control and Inverse Problems
Assoc. Prof. Patrick E. Farrell, University of Oxford, UK:
Computing disconnected bifurcation diagrams of partial differential equations
more ... Location
Online Event

Abstract
Computing the distinct solutions u of an equation f(u, lambda)=0 as a parameter lambda in IR is varied is a central task in applied mathematics and engineering. The solutions are captured in a bifurcation diagram, plotting (some functional of) u as a function of lambda. In this talk I will present a new algorithm, deflated continuation, for this task. Deflated continuation has three advantages. First, it is capable of computing disconnected bifurcation diagrams; previous algorithms only aimed to compute that part of the bifurcation diagram continuously connected to the initial data. Second, its implementation is very simple: it only requires a minor modification to an existing Newton-based solver. Third, it can scale to very large discretisations if a good preconditioner is available; no auxiliary problems must be solved. We will present applications to hyperelastic structures, liquid crystals, and Bose-Einstein condensates, among others.

Further Informations
Berlin Oberseminar: Optimization, Control and Inverse Problems

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 30.06.2021, 15:15 (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Stefanie Schindler, WIAS Berlin:
Self-similar diffusive equilibration for a coupled reaction-diffusion system with mass-action kinetics (online talk)
more ... Location
Online Event

Abstract
We study a coupled system of two nonlinear reaction-diffusion equations on the unbounded domain ℝ, where we consider reaction kinetics of the reaction nX1 ⇌ mX2 according to the mass-action law. We show the global existence and uniqueness of classical solutions and prove the existence of invariant rectangles, that is, bounded regions ∑ ⊂ ℝ2 in which the solutions stay for all times, provided that the initial data lies entirely in ∑. Further, by assuming that the reaction is equilibrated and that the asymptotic boundary conditions at infinity are given by constant steady-state solutions, the diffusive mixing is studied. Here the theory of self-similar solutions in the sense of Barenblatt is applicable. Combined with the theory of monotone operators, this enables us to prove that there exists for each choice of asymptotic boundary conditions a similarity profile. This research is joint work with Alexander Mielke.

Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 29.06.2021, 15:15 (Online Event)
Oberseminar Nonlinear Dynamics
Prof. Sebastian Wieczorek, University College Cork:
Rate-induced tipping points (online talk)
more ... Location
Online Event

Abstract
Many systems are subject to external disturbances or changing external conditions. For a system near a stable state (an attractor) we might expect that, as external conditions change with time, the stable state will change too. In many cases the system may adapt to changing external conditions and track the moving stable state. However, tracking may not always be possible owing to nonlinearities and feedbacks in the system. So far, the focus has been on critical levels of external conditions (dangerous autonomous bifurcation points) where the stable state turns unstable or disappears, causing the system to suddenly move to a different and often undesired state. We describe this phenomenon as bifurcation-induced tipping or B-tipping. However, critical levels are not the only critical factor for tipping. Some systems can be particularly sensitive to how fast the external conditions change and have critical rates: they suddenly and unexpectedly move to a different state if the external input changes too fast. This happens even though the moving stable state never loses stability in the classical autonomous sense! We describe this phenomenon as rate-induced tipping or R-tipping. Being a genuine non-autonomous bifurcation, R-tipping is not captured by the classical bifurcation theory and requires an alternative framework. In the first part of the talk, we demonstrate R-tipping in a simple ecosystem model where environmental changes are represented by time-varying parameters. We then introduce the concept of basin instability and show how to complement the classical bifurcation diagram with information on nonautonomous R-tipping that cannot be captured by the classical bifurcation analysis. In the second part of the talk, we develop a general mathematical framework for R-tipping with decaying inputs based on the concepts of thresholds, edge states and special compactification of the nonautonomous system. This allows us to transform the R-tipping problem into a connecting heteroclinic orbit problem in the compactified system, which greatly simplifies the analysis. We explain the key concept of threshold instability and give rigorous testable criteria for R-tipping to occur in arbitrary dimension. In the third part of the talk, we discuss the so-called “compost-bomb instability", which is an example of R-tipping without an obvious threshold. We use geometric singular perturbation theory and desingularisation to reveal non-obvious R-tipping thresholds and edge states.

Host
Freie Universität Berlin
WIAS Berlin
Tuesday, 29.06.2021, 10:15 (Online Event)
Seminar Nichtlineare Optimierung und Inverse Probleme
Dr. Ingo Bremer, WIAS Berlin:
Parameterbestimmung zur Anpassung des SEIR-Models an Covid-19 Zeitreihen
more ... Location
Online Event

Further Informations
You can follow this talk by zoom: https://zoom.us/j/98493865627.

Host
WIAS Berlin
Thursday, 24.06.2021, 13:00 (Online Event)
Seminar Numerische Mathematik
Felipe Galarce Marín, WIAS Berlin:
Inverse problems in haemodynamics. Fast estimation of blood flows on non-parametric domains from medical data
more ... Location
Online Event

Abstract
This seminar presents a work at the interface between applied mathematics and biomedical engineering. The work's main subject is the estimation of blood flows and quantities of medical interest in diagnosing certain diseases concerning the cardiovascular system. We propose a complete pipeline, providing the theoretical foundations for state estimation from medical data using reduced-order models, and addressing inter-patient variability. Extensive numerical tests are shown in realistic 3D scenarios that verify the potential impact of the work in the medical comunnity.

Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de

Host
WIAS Berlin
Wednesday, 23.06.2021, 15:15 (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Martin Brokate, Technische Universität München:
A variational inequality for the derivative of the play operator (online talk)
more ... Location
Online Event

Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 23.06.2021, 11:30 (Online Event)
Seminar Interacting Random Systems
Tejas Iyer, WIAS Berlin:
Degree and Edge Distributions in Inhomogeneous Random Recursive Trees (online talk)
more ... Location
Online Event

Abstract
We introduce general models of inhomogeneous random recursive trees, where either one or several nodes arrive at a time, and are equipped with i.i.d random weights. At each time-step, an existing vertex is chosen with probability proportional to its fitness function, and the newly arriving node(s) connect to it. This may be a function of its weight, and possibly the weights of its neighbours. We study two main quantities: the empirical measures associated with the number of vertices with a given degree and weight and the empirical measure corresponding proportion of edges in the structure with endpoint having a given weight. We show that, under certain technical conditions, the limit of both quantities exists when normalised by the size of the network, as the number of nodes tends to infinity. However, when the trees take certain forms, we show that interesting, non-trivial behaviour can emerge when these conditions fail: in particular, the trees may exhibit emphcondensation where a positive proportion of edges accumulate around vertices with weight that maximises the reinforcement of their fitness, or, more drastically, may have a emphdegenerate limiting degree distribution where the entire proportion of edges accumulate around these vertices. This non-trivial behaviour may be of interest when considering the trees as toy models for the evolution of complex networks.

Further Informations
Seminar Interacting Random Systems (Online Event)

Host
WIAS Berlin
Tuesday, 22.06.2021, 15:15 (Online Event)
Oberseminar Nonlinear Dynamics
Bhumika Thakur, Jacobs University, Bremen:
Data driven identification of nonlinear dynamics using sparse regression with applications in plasma physics
more ... Location
Online Event

Abstract
Data driven techniques are increasingly finding applications in physical sciences and plasma physics is no exception. Many plasma processes are highly complex and nonlinear and often the exact form of the equations governing their dynamics is not known. If we can construct these equations from the experimental data, then we can further our understanding of these processes and use techniques such as model reduction to isolate dominant physical mechanisms. A large number of regression techniques are available for identification of system dynamics from data, with varying degrees of generality and complexity. Sparse identification of nonlinear dynamics (SINDy) algorithm is one such technique that can be used to find parsimonious models. I will talk about this algorithm and discuss some examples where it is being applied in plasma physics with a focus on our ongoing attempt at finding the model equations for anode glow oscillations observed in a glow discharge plasma device.

Host
Freie Universität Berlin
WIAS Berlin
Wednesday, 16.06.2021, 12:30 (Online Event)
Forschungsseminar Mathematische Statistik
Prof. Irène Gijbels, KU Leuven, Netherlands:
Extremiles and extremile regression (online talk)
more ... Location
Online Event

Abstract
Quantiles and expectiles of a distribution are found to be useful descriptors of its tail in the same way as the median and mean are related to its central behavior. In this talk we discuss an alternative class to expectiles, called extremiles. The new class is motivated via several angles, which reveals its speci c merits and strengths. Extremiles suggest better capability of tting both location and spread in data points and provide an appropriate theory that better displays the interesting features of long-tailed distributions. We brie y discuss estimation of extremiles. A large part of the talk will be on regression extremiles, which thus de ne a least squares analogue of regression quantiles.We discuss estimation of conditional extremiles, in which we rely on local linear (least squares) checkfunction minimization. An asymptotic normality result for the estimators is established. Attention also goes to extending extremile regression far into the tails of heavy-tailed distributions. For this purpose extrapolated estimators are constructed and their asymptotic theory is developed. Applications to real data illustrate how extremiles and related tools can be used in practice.)

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
WIAS Berlin
June 16 – 18, 2021 (Online Event)
Workshop/Konferenz: Nonlinear Dynamics in Semiconductor Lasers
more ... Location
Online Event

Host
WIAS Berlin
Tuesday, 15.06.2021, 15:15 (Online Event)
Oberseminar Nonlinear Dynamics
Philipp Lorenz-Spreen, MPI for Human Development, Berlin:
Modeling radicalization dynamics and polarization in temporal networks
more ... Location
Online Event

Abstract
Echo chambers and opinion polarization have been recently quantified in several sociopolitical contexts, across different social media, raising concerns for the potential impact on the spread of misinformation and the openness of debates. Despite increasing efforts, the dynamics leading to the emergence of these phenomena remain unclear. Here, we propose a model that introduces the phenomenon of radicalization, as a reinforcing mechanism driving the evolution to extreme opinions from moderate initial conditions. Empirically inspired by the dynamics of social interaction, we consider agents characterized by heterogeneous activities and homophily. We analytically characterize the transition from a global consensus to an emerging radicalization that depends on parameters, which can be interpreted as the controversialness of a topic and the strength of social influence people exert on each other. Finally, we offer a definition of echo-chambers via our model and contrast the model's behavior against empirical data of polarized debates on Twitter, qualitatively reproducing the observed relation between users' engagement and opinions, as well as opinion segregation based on the interaction network. Our findings shed light on the dynamics that may lie at the core of the emergence of echo chambers and polarization in social media.

Host
Freie Universität Berlin
WIAS Berlin
Tuesday, 15.06.2021, 15:00 (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Lennard Henze, Humboldt-Universität zu Berlin:
Classification of quantum dot images using machine learning (online talk)
more ... Location
Online Event

Abstract
A possibility of classifying quantum dot images obtained out of a simulation using a machine learning algorithm and image augmentation techniques is explored. The results on the similar MNIST data set suggest that a classification using machine learning techniques is indeed possible. Furthermore, a theoretical result concerning the extrapolation properties of artificial neural networks will be presented.

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Tuesday, 15.06.2021, 10:15 (Online Event)
Seminar Nichtlineare Optimierung und Inverse Probleme
Maximilian Reiter, TU Berlin:
Numerical approximation of the Ericksen--Leslie equations (online talk)
more ... Location
Online Event

Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/98493865627.

Host
WIAS Berlin
Monday, 14.06.2021, 15:00 (Online Event)
Berlin Oberseminar: Optimization, Control and Inverse Problems
Dr. Ozan Öktem, KTH Royal Institute of Technology, Stockholm:
Data driven large-scale convex optimisation
more ... Location
Online Event

Abstract
This joint work with Jevgenjia Rudzusika (KTH), Sebastian Banert (Lund University) and Jonas Adler (DeepMind) introduces a framework for using deep-learning to accelerate optimisation solvers with convergence guarantees. The approach builds on ideas from the analysis of accelerated forward-backward schemes, like FISTA. Instead of the classical approach of proving convergence for a choice of parameters, such as a step-size, we show convergence whenever the update is chosen in a specific set. Rather than picking a point in this set through a handcrafted method, we train a deep neural network to pick the best update. The method is applicable to several smooth and non-smooth convex optimisation problems and it outperforms established accelerated solvers.

Host
WIAS Berlin
Wednesday, 09.06.2021, 15:15 (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Julian Fischer, Institute of Science and Technology Austria (IST Austria):
Uniqueness and stability properties of multiphase mean curvature flow: An approach based on the variational (gradient flow) structure of the problem (online talk)
more ... Location
Online Event

Abstract
For many evolution problems for interfaces - like for instance multiphase mean curvature flow or the Mullins--Sekerka equation - appropriate weak solutions are known to exist globally in time, but the uniqueness of such weak solutions is either unknown or even known to fail. At the same time, due to geometric singularities strong solution concepts are in general limited to local in time existence results. In the absence of a comparison principle, the relation between weak and strong solutions for interface evolution problems has remained a mostly open question. We establish a weak-strong uniqueness principle for planar multiphase mean curvature flow: We prove that for mean curvature flow of planar networks,there is only a single BV solution prior to the first topology change. Our approach relies on the variational structure of mean curvature flow, being the gradient flow of the interface energy functional. For many minimization problems for interface energy functionals, the method of calibrations has made it possible to deduce the uniqueness of minimizers. Our approach to weak-strong uniqueness for mean curvature flow relies on a novel gradient-flow analogue of this concept of calibrations, basically allowing us to show that the route of steepest descent in the energy landscape is unique and stable with respect to perturbations. In the last part of the talk, we will discuss possible future applications of our concept, including the quantitative convergence of phase-field approximations for mean curvature flow.

Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 09.06.2021, 11:30 (Online Event)
Seminar Interacting Random Systems
Wen Sun, TU Berlin:
Pathwise large deviation for the pure jump k-nary interacting particle systems (online talk)
more ... Location
Online Event

Abstract
A pathwise large deviation result is proved for the pure jump models of k-nary interacting particle system introduced by Kolokoltsov that generalize classical Boltzmann's collision model, Smoluchovski's coagulation model and many others. The upper bound is obtained by following the standard methods of using a process "perturbed" by a regular function. To show the lower bound, we propose a family of orthogonal martingale measures and prove a coupling for the general perturbations. The rate function is studied based on the idea of Léonard with a simplification by considering the conjugation of integral functionals on a subspace of L^infty.. General "gelling" solutions in the domain of the rate function are also discussed.

Further Informations
Seminar Interacting Random Systems (Online Event)

Host
WIAS Berlin
Tuesday, 08.06.2021, 15:15 (Online Event)
Oberseminar Nonlinear Dynamics
Chunming Zheng, MPI for Physics of Complex Systems, Dresden:
Transition to synchrony in the three-dimensional Noisy Kuramoto model
more ... Location
Online Event

Abstract
We investigate the transition from incoherence to global collective motion in a three-dimensional swarming model of agents with helical trajectories, subject to noise and global coupling. Without noise this model was recently proposed as a generalization of the Kuramoto model and it was found, that alignment of the velocities occurs for arbitrary small attractive coupling. Adding noise to the system resolves this singular limit.

Host
Freie Universität Berlin
WIAS Berlin
Tuesday, 01.06.2021, 15:15 (Online Event)
Oberseminar Nonlinear Dynamics
Dr. Georgi Medvedev, Drexel University:
Unfolding chimeras: Where Turing meets Penrose (online talk)
more ... Location
Online Event

Abstract
The coexistence of coherence and incoherence is arguably the most interesting effect in the theory of synchronization and possibly in nonlinear science in general discovered in the past two decades. Despite intense research chimera states still present many challenging questions to the nonlinear science community. There is no consensus on how to define chimera states. Further, the theory is only available for chimera states lying in the Ott--Antonsen manifold, which is an elegant but a very special case. In this work, we suggest a new way for studying chimera states based on the combination of the linear stability analysis of mixing and a beautiful method of Penrose for Vlasov equation in plasma physics. This approach yields a new qualitative description of chimera states and provides very accurate quantitative estimates. Our results are universal in the sense that the structure and bifurcations of chimera states are explained in terms of the qualitative properties of the distribution of intrinsic frequencies and network topology, and, thus, are relevant for interacting particle systems of all scales from neuronal networks, to power grids, to astrophysics. This talk is based on the joint work with Hayato Chiba (Tohoku University) and Matthew Mizuhara (The College of New Jersey).

Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://us02web.zoom.us/j/84203723799?pwd=bmNVcVBaazRzSlI3TjAxV1U1S2xFQT09

Host
Freie Universität Berlin
WIAS Berlin
May 31 – June 2, 2021 (Online Event)
Workshop/Konferenz: SPDEs and their friends
more ... Location
Online Event

Host
WIAS Berlin
Technische Universität Berlin
Wednesday, 26.05.2021, 15:15 (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Riccarda Rossi, Università degli Studi di Brescia, Italien:
Jump processes as generalized gradient systems (online talk)
more ... Location
Online Event

Abstract
The approach à la Jordan-Kinderlehrer-Otto to a vast class of evolutionary problems, interpreted as gradient flows in Wasserstein spaces, was extended by Maas and Mielke to Markov chains via the introduction of Benamou-Brenier type distances. Nonetheless, the study of the microscopic origin of jump processes by means of large deviations theory suggests that such processes possess a generalized gradient system structure based on non-homogeneous dissipation potentials that do not give rise to any metric structure. This talk revolves around the generalized gradient system structure that we have proposed for these processes in collaboration with Mark Peletier, Giuseppe Savaré and Oliver Tse. To build it, we have introduced a suitable `dynamical-variational' transport cost that induces a notion of length. Based on it, we can set forth an extended version of the Minimizing Movement scheme. We show the convergence of the discrete solutions arising from the time-incremental minimization scheme, to a curve fulfilling a suitable `non-metric' gradient flow formulation for the original jump process.

Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 26.05.2021, 11:30 (Online Event)
Seminar Interacting Random Systems
András Tóbiás, TU Berlin:
Absence of percolation in graphs based on stationary point processes with degrees bounded by two (online talk)
more ... Location
Online Event

Abstract
We consider undirected graphs that arise as deterministic functions of stationary point processes such that each point has degree bounded by two. For a large class of point processes and edge-drawing rules, we show that the arising graph has no infinite connected component, almost surely. In particular, this extends our previous result for SINR graphs based on stabilizing Cox point processes and verifies the conjecture of Balister and Bollobás that the bidirectional k-nearest neighbor graph of a two-dimensional homogeneous Poisson point process does not percolate for k=2. The subject of this talk is joint work with B. Jahnel.

Further Informations
Seminar Interacting Random Systems (Online Event)

Host
WIAS Berlin
Wednesday, 26.05.2021, 09:00 (Online Event)
Forschungsseminar Mathematische Statistik
Prof. Hans-Georg Müller, University of California, Davis, USA:
Functional models for time-varying random objects (online talk)
more ... Location
Online Event

Abstract
In recent years, samples of random objects and time-varying object data such as time-varying distributions or networks that are not in a vector space have become increasingly prevalent. Such data can be viewed as elements of a general metric space that lacks local or global linear structure. Common approaches that have been used with great success for the analysis of functional data, such as functional principal component analysis, are therefore not applicable. The concept of metric covariance makes it possible to define a metric auto-covariance function for a sample of random curves that take values in a general metric space and it can be shown to be non-negative definite when the squared semi-metric of the underlying space is of negative type. Then the eigenfunctions of the linear operator with the auto-covariance function as kernel can be used as building blocks for an object functional principal component analysis, which includes real-valued Frechet scores and metric-space valued object functional principal components. Sample based estimates of these quantities are shown to be asymptotically consistent and are illustrated with various data. (Joint work with Paromita Dubey, Stanford University.)

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Thursday, 20.05.2021, 14:00 (Online Event)
Seminar Numerische Mathematik
Prof. Thomas Richter, Universität Magdeburg:
Deep neural networks for accelerating fluid-dynamics simulations
more ... Location
Online Event

Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de

Host
WIAS Berlin
Wednesday, 19.05.2021, 15:15 (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Alexander Mielke, WIAS Berlin, Humboldt-Universität zu Berlin:
Towards a justification of GENERIC: coarse-graining of an infinite-dimensional Hamiltonian system (online talk)
more ... Location
Online Event

Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 19.05.2021, 10:00 (Online Event)
Forschungsseminar Mathematische Statistik
Prof. Hannes Leeb, University of Vienna, Österreich:
A (tight) upper bound for the length of confidence intervals with conditional coverage
more ... Location
Online Event

Abstract
We show that two popular selective inference procedures, namely data carving (Fithian et al., 2017) and selection with a randomized response (Tian et al., 2018b), when combined with the polyhedral method (Lee et al., 2016), result in confidence intervals whose length is bounded. This contrasts results for confidence intervals based on the polyhedral method alone, whose expected length is typically infinite (Kivaranovic and Leeb, 2020). Moreover, we show that these two procedures always dominate corresponding sample-splitting methods in terms of interval length.

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 12.05.2021, 15:15 (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Thomas Eiter, WIAS Berlin:
Leray--Hopf solutions to a viscoelastic fluid model with nonsmooth stress-strain relation (online talk)
more ... Location
Online Event

Abstract
Subject of the talk is a fluid model including viscoelastic and viscoplastic effects. The state is given by the fluid velocity and an internal stress tensor that is transported along the flow with the Zaremba--Jaumann derivative. Moreover, the stress tensor obeys a nonlinear and nonsmooth dissipation law as well as stress diffusion. After a discussion of the model, the existence of global-in-time weak solutions, which satisfy an energy inequality, is shown under general Dirichlet conditions for the velocity field and Neumann conditions for the stress tensor.

Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 12.05.2021, 11:30 (Online Event)
Seminar Interacting Random Systems
Tal Orenshtein, WIAS Berlin/TU Berlin:
Rough walks in random environment
more ... Location
Online Event

Abstract
Random walks in random environment (RWRE) have been extensively studied in the last half-century. Functional central limit theorems (FCLT) hold in some prototypical classes such the reversible and the ballistic ones. The latter are treated using rather different techniques; Kipnis-Varadhan's theory for additive functionals of Markov processes is applicable in the reversible case whereas the main feature exploited in the ballistic class is a regeneration structure. Rough path theory is a deterministic theory which extends classical notions of integration to singular integrators in a continuous manner. It typically provides a framework for pathwise solutions of ordinary and partial stochastic differential equations driven by a singular noise. In the talk we shall discuss FCLT for additive functionals of Markov processes and regenerative processes lifted to the rough path space. The limiting rough path has two levels. The first one is the Brownian motion, whereas in the second we see a new feature: it is the iterated integral of the Brownian motion perturbed by a deterministic linear function called the area anomaly. The aforementioned classes of RWRE are covered as special cases. The results provide sharper information on the limiting path. In addition, the construction of new examples for SDE approximations is an immediate application. Based on collaborations (some are still in progress) with Johannes Bäumler, Noam Berger, Jean-Dominique Deuschel, Olga Lopusanschi, Nicolas Perkowski and Martin Slowik.

Further Informations
Seminar Interacting Random Systems (Online Event)

Host
WIAS Berlin
Tuesday, 11.05.2021, 15:15 (Online Event)
Oberseminar Nonlinear Dynamics
Alicia Dickenstein, U Buenos Aires:
Algebra and geometry in the study of enzymatic networks? (online talk)
more ... Location
Online Event

Abstract
I will try to show in my lecture that the question in the title has a positive answer, summarizing recent mathematical results about signaling networks in cells obtained with algebro-geometric tools.

Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://us02web.zoom.us/j/84203723799?pwd=bmNVcVBaazRzSll3TjAxV1U1S2xFQT09.

Host
Freie Universität Berlin
WIAS Berlin
Tuesday, 11.05.2021, 15:00 (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Paul Hager, Technische Universität Berlin:
Optimal stopping with signatures (online talk)
more ... Location
Online Event

Abstract
We propose a new method for solving optimal stopping problems (such as American option pricing in finance) under minimal assumptions on the underlying stochastic process. We consider classic and randomized stopping times represented by linear and non-linear functionals of the rough path signature associated to the underlying process, and prove that maximizing over these classes of signature stopping times, in fact, solves the original optimal stopping problem. Using the algebraic properties of the signature, we can then recast the problem as a (deterministic) optimization problem depending only on the (truncated) expected signature. By applying a deep neural network approach to approximate the non-linear signature functionals, we can efficiently solve the optimal stopping problem numerically. The only assumption on the underlying process is that it is a continuous (geometric) random rough path. Hence, the theory encompasses processes such as fractional Brownian motion, which fail to be either semi-martingales or Markov processes, and can be used, in particular, for American-type option pricing in fractional models, e.g. on financial or electricity markets. This is a joint work with Christian Bayer, Sebastian Riedel and John Schoenmakers.

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Tuesday, 04.05.2021, 15:15 (Online Event)
Oberseminar Nonlinear Dynamics
Dr. Maximilian Engel, FU Berlin:
Lyapunov exponents in random dynamical systems and how to find and use them
more ... Location
Online Event

Abstract
This talk aims to give an overview on various notions of Lyapunov exponents (LEs) in random dynamical systems, that is, systems whose evolution in time is governed by laws exhibiting randomness: from finite-time LEs to classical asymptotic LEs and corresponding spectra up to LEs for processes conditioned on staying in bounded domains. We demonstrate how these notions, especially of a first, dominant LE, become relevant in the context of stochastic bifurcations, in finite and infinite dimensions.

Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/84203723799.

Host
Freie Universität Berlin
WIAS Berlin
Monday, 03.05.2021, 15:00 (Online Event)
Berlin Oberseminar: Optimization, Control and Inverse Problems
Assoc. Prof. Lars Ruthotto, Emory University, USA:
A machine learning framework for mean field games and optimal control
more ... Location
Online Event

Abstract
We consider the numerical solution of mean field games and optimal control problems whose state space dimension is in the tens or hundreds. In this setting, most existing numercial solvers are affected by the curse of dimensionality (CoD). To mitigate the CoD, we present a machine learning framework that combines the approximation power of neural networks with the scalability of Lagrangian PDE solvers. Specifically, we parameterize the value function with a neural network and train its weight using the objective function with additional penalties that enforce the Hamilton Jacobi Bellman equations. A key benefit of this approach is that no training data is needed, e.g., no numerical solutions to the problem need to be computed before training. We illustrate our approach and its efficacy using numerical experiments. To show the framework's generality, we consider applications such as optimal transport, deep generative modeling, mean field games for crowd motion, and multi-agent optimal control.

Host
WIAS Berlin
April 29, 2021 (Online Event)
Workshop/Konferenz: FUHRI2021: Finite volUme metHods for Real-world applIcations
more ... Location
Online Event

Host
WIAS Berlin
Wednesday, 28.04.2021, 15:15 (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Katharina Hopf, WIAS Berlin:
Weak-strong uniqueness in energy-reaction-diffusion systems (online talk)
more ... Location
Online Event

Abstract
We establish weak-strong uniqueness and stability properties of renormalised solutions to a class of energy-reaction-diffusion systems, which genuinely feature cross-diffusion effects. The systems considered are motivated by thermodynamically consistent models, and their formal entropy structure allows us to use as a key tool a suitably adjusted relative entropy method. Weak-strong uniqueness is obtained for general entropy-dissipating reactions without growth restrictions, and certain models with a non-integrable diffusive flux. The results also apply to a class of (isoenergetic) reaction-cross-diffusion systems.

Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 28.04.2021, 11:30 (Online Event)
Seminar Interacting Random Systems
Alexander Hinsen, WIAS Berlin:
Percolation on a dynamical device-to-device communication system (online talk)
more ... Location
Online Event

Abstract
We model a system of moving devices on a street system with the help of a general waypoint kernel. If there is an uninterrupted communication window between devices (their space-time trajectories are close to each other) they form a connection. We study regimes for percolation and absence of percolation of the cluster of connected devices, as it can be seen as an indication for the ability of the system to transmit messages over long distances.

Further Informations
Seminar Interacting Random Systems (Online Event)

Host
WIAS Berlin
Tuesday, 27.04.2021, 15:15 (Online Event)
Oberseminar Nonlinear Dynamics
Eddie Nijholt, University of Illinois, USA:
Exotic symmetry in networks
more ... Location
Online Event

Abstract
Network dynamical systems appear all throughout science and engineering. Despite this prevalence, it remains unclear precisely how network structure impacts the dynamics. One very successful approach in answering this question is by identifying symmetry. Of course, there are many networks that do not have any form of symmetry, yet which still show remarkable dynamical behavior. Instead a wide array of other network features (such as node-dependency, synchrony spaces, and so forth) are known to impact the dynamics. We will see that most of these features can still be captured as symmetry, provided one widens the definition. That is, instead of considering classical group symmetry, one has to allow for more “exotic structures”, such as semigroups, categories and quivers. In many cases the network topology itself can even be seen as such a symmetry. An important consequence is that network structure can therefore be preserved in most reduction techniques, which in turn makes it possible to analyse bifurcations in such systems. In order to best explain these notions, l do not assume any familiarity with group symmetry -or their exotic counterparts- on the part of the audience.

Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/84203723799.

Host
Freie Universität Berlin
WIAS Berlin
Tuesday, 27.04.2021, 15:00 (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Prof. Peter Friz, WIAS Berlin, TU Berlin:
New perspectives on rough paths, signatures and signature cumulants (online talk)
more ... Location
Online Event

Abstract
We revisit rough paths and signatures from a geometric and “smooth model" perspective. This provides a lean framework to understand and formulate key concepts of the theory, including recent insights on higher-order translation a.k.a. renormalization of rough paths. This first part is joint work with C. Bellingeri (TU Berlin), and S. Paycha (U Potsdam). In a second part, we take a semimartingale perspective and more specifically analyze the structure of expected signatures when written in exponential form. Following Bonnier-Oberhauser (2020), we call the resulting objects signature cumulants. These can be described - and recursively computed - in a way that can be seen as unification of previously unrelated pieces of mathematics, including Magnus (1954), Lyons-Ni (2015), Gatheral and coworkers (2017 onwards) and Lacoin-Rhodes-Vargas (2019). This is joint work with P. Hager and N. Tapia.

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Tuesday, 27.04.2021, 10:00 (Online Event)
Seminar Numerische Mathematik
Prof. Sashikumaar Ganesan, Indian Institute of Science Bangalore; Prof. Volker John, WIAS Berlin:
Minisymposium on machine learning
more ... Location
Online Event

Further Informations
For zoom login details please contact Volker John john@wias-berlin.de

Host
WIAS Berlin
Wednesday, 21.04.2021, 15:15 (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Nikolas Nüsken, Universität Potsdam:
The Stein geometry in machine learning: gradient flows, large deviations and convergence properties (online talk)
more ... Location
Online Event

Abstract
Sampling or approximating high-dimensional probability distributions is a key challenge in computational statistics and machine learning. This talk will present connections to gradient flow PDEs and interacting particle systems, focusing on the recently introduced Stein variational gradient descent methodology. The construction induces a novel geometrical structure on the set of probability distributions related to a positive definite kernel function.We discuss the corresponding geodesic equations as well as large deviation functionals and leverage those to shed some light on the convergence properties of the algorithm. This is joint work with A. Duncan (Imperial College London), L. Szpruch (University of Edinburgh) and M. Renger (Weierstrass Institute Berlin).

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 20.04.2021, 15:15 (Online Event)
Oberseminar Nonlinear Dynamics
Alan Rendall, Johannes Gutenberg-Universität Mainz:
Bogdanov--Takens bifurcations and the regulation of enzymatic activity by autophosphorylation
more ... Location
Online Event

Abstract
An important mechanism of information storage in molecular biology is the binding of phosphate groups to proteins. In this talk we consider the case of autophosphorylation, where the protein is an enzyme and the substrate to which it catalyses the binding of a phosphate group is that enzyme itself. It turns out that this often leads to more complicated dynamics than those seen in the case where enzyme and substrate are distinct. We focus on the example of the enzyme Lck (lymphocyte-associated tyrosine kinase) which is of central importance in the function of immune cells. We study a model for the activation of Lck due to Kaimachnikov and Kholodenko and give a rigorous proof that it admits periodic solutions. We do so by showing that it exhibits a generic Bogdanov-Takens bifurcation. This is an example where this approach gives a simpler proof of the existence of periodic solutions than ones

Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/84203723799.

Host
Freie Universität Berlin
WIAS Berlin
Tuesday, 20.04.2021, 15:00 (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Caroline Geiersbach, WIAS Berlin:
Stochastic approximation with applications to PDE-constrained optimization under uncertainty (online talk)
more ... Location
Online Event

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Thursday, 15.04.2021, 14:00 (Online Event)
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Steven-Marian Stengl, WIAS Berlin:
Combined regularization and discretization of equilibrium problems and primal-dual gap estimators
more ... Location
Online Event

Abstract
In this talk, we address the treatment of finite element discretizations of a class of equilibrium problems involving moving constraints. Therefore, a Moreau-Yosida based regularization technique, controlled by a parameter, is discussed. A generalized Gamma-convergence concept is utilized to obtain a priori results. The same technique is applied to the discretization and the combination of both. In addition, a primal-dual gap technique is used for the derivation of error estimators and a strategy for balancing between a refinement of the mesh and an update of the regularization parameter is established. The theoretical findings are illustrated for the obstacle problem as well as numerical experiments are performed for two quasi-variational inequalities with application to thermoforming and biomedicine, respectively.

Further Informations
Seminar Mathematical Optimization / Non-smooth Variational Problems and Operator Equations

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Thursday, 15.04.2021, 14:00 (Online Event)
Seminar Numerische Mathematik
Prof. Julia Novo, Universidad Autónoma de Madrid, Spanien:
Error analysis of proper orthogonal decomposition stabilized methods for incompressible flows
more ... Location
Online Event

Abstract
Proper orthogonal decomposition (POD) stabilized methods for the Navier-Stokes equations are presented. We consider two cases: the case in which the snapshots are based on a non inf-sup stable method and the case in which the snapshots are based on an inf-sup stable method. For both cases we construct approximations to the velocity and the pressure. For the first case, we analyze a method in which the snapshots are based on a stabilized scheme with equal order polynomials for the velocity and the pressure with local projection stabilization (LPS) for the gradient of the velocity and the pressure. For the POD method we add the same kind of LPS stabilization for the gradient of the velocity and the pressure as the direct method, together with grad-div stabilization. In the second case, the snapshots are based on an inf-sup stable Galerkin method with grad-div stabilization and for the POD model we also apply grad-div stabilization. In this case, since the snapshots are discretely divergence-free, the pressure can be removed from the formulation of the POD approximation to the velocity. To approximate the pressure, needed in many engineering applications, we use a supremizer pressure recovery method. Error bounds with constants independent of inverse powers of the viscosity parameter are proved for both methods. Numerical experiments show the accuracy and performance of the schemes.

Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de

Host
WIAS Berlin
Wednesday, 14.04.2021, 15:15 (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Flaviana Iurlano, Sorbonne Université Paris, Frankreich:
Shape optimization of light structures (online talk)
more ... Location
Online Event

Abstract
We prove rigorous results about the vanishing-mass limit of the classical problem to find a shape with minimal elastic compliance. Contrary to all previous results in the mathematical literature, which utilize a soft mass constraint by introducing a Lagrange multiplier, we here consider the hard mass constraint. Our results are the first to establish the convergence of approximately optimal shapes of (exact) size $varepsilonto 0$ to a limit generalized shape represented by a (possibly diffuse) probability measure. This limit generalized shape is a minimizer of the limit compliance, which involves a new integrand, namely the one conjectured by Bouchitté in 2001 and predicted heuristically before in works of Allaire & Kohn and Kohn & Strang from the 1980s and 1990s. This integrand gives the energy of the limit generalized shape understood as a fine oscillation of (optimal) lower-dimensional structures. Its appearance is surprising since the integrand in the original compliance is just a quadratic form and the non-convexity of the problem is not immediately obvious. In fact, it is the interaction of the mass constraint with the requirement of attaining the loading (in the form of a divergence-constraint) that gives rise to this new integrand. Our proofs rest on compensated compactness arguments applied to an explicit family of div-quasiconvex quadratic forms, computations involving the Hashin--Shtrikman bounds for the Kohn--Strang integrand, and the characterization of limit minimizers due to Bouchitté & Buttazzo.

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 14.04.2021, 11:30 (Online Event)
Seminar Interacting Random Systems
Alexis Prevost, University of Cambridge, GB:
Cluster capacity functionals and isomorphism theorems for Gaussian free fields (online talk)
more ... Location
Online Event

Abstract
Various isomorphisms theorem relate Gaussian free fields to random walk models, through their local times. Among them, the second Ray-Knight theorem can be extended in an isomorphism between the Gaussian free field and random interlacements on transient graphs. Following the work of Lupu and Sznitman, we will explain how the cable system method let us make this isomorphism more explicit, and how it relates to a certain cluster capacity functional for the Gaussian free field. Finally, we will present applications to percolation for the Gaussian free field on the cable system. Joint work with Alexander Drewitz (Cologne) and Pierre-François Rodriguez (London)

Further Informations
Seminar Interacting Random Systems (Online Event)

Host
WIAS Berlin
Tuesday, 13.04.2021, 16:00 (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Yangwen Sun, Humboldt-Universität zu Berlin:
Graph-spanning ratio test with application to change-point detection problem (online talk)
more ... Location
Online Event

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Tuesday, 30.03.2021, 10:15 (Online Event)
Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Dr. Simona Perotto, Politecnico di Milano, Italien:
Adaptive topology optimization in the design of structures and metamaterials (online talk)
more ... Location
Online Event

Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/98493865627.

Host
WIAS Berlin
Monday, 29.03.2021, 15:00 (Online Event)
Berlin Oberseminar: Optimization, Control and Inverse Problems
Prof. Serge Gratton, ENSEEIHT, Toulouse, France:
On a multilevel Levenberg--Marquardt method for the training of artificial neural networks and its application to the solution of partial differential equations (online talk)
more ... Location
Online Event

Abstract
We propose a new multilevel Levenberg--Marquardt optimizer for the training of artificial neural networks with quadratic loss function. When the least-squares problem arises from the training of artificial neural networks, the variables subject to optimization are not related by any geometrical constraints and the standard interpolation and restriction operators cannot be employed any longer. A heuristic, inspired by algebraic multigrid methods, is then proposed to construct the multilevel transfer operators. We test the new optimizer on an important application: the approximate solution of partial differential equations by means of artificial neural networks. The learning problem is formulated as a least-squares problem, choosing the nonlinear residual of the equation as a loss function, whereas the multilevel method is employed as a training method. Numerical experiments show encouraging results related to the efficiency of the new multilevel optimization method compared to the corresponding one-level procedure in this context.

Further Informations
Seminar on Optimization, Control and Inverse Problems

Host
WIAS Berlin
Thursday, 25.03.2021, 14:00 (Online Event)
Seminar Numerische Mathematik
Benoît Gaudeul, Université de Lille, France:
Two entropic finite volume schemes for a Nernst--Planck--Poisson system with ion volume constraints
more ... Location
Online Event

Abstract
In this talk, I consider a drift-diffusion system with cross-coupling through the chemical potentials comprising a model for the motion of finite size ions in liquid electrolytes. The drift term is due to the self-consistent electric field maintained by the ions and described by a Poisson equation.
I present two finite volume schemes based on different formulations of the fluxes. I will also provide a stability analysis of these schemes and an existence result for the corresponding discrete solutions. A convergence result is proposed for non-degenerate solutions. Numerical experiments show the behavior of these schemes.
This is a joint work with Jürgen Fuhrmann.

Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de

Host
WIAS Berlin
Thursday, 18.03.2021, 14:00 (Online Event)
Seminar Numerische Mathematik
Prof. Leo Rebholz, Clemson University, USA:
Anderson acceleration and how it speeds up convergence in fixed point iterations
more ... Location
Online Event

Abstract
Anderson acceleration (AA) is an extrapolation technique originally proposed in 1965 that recombines the most recent iterates and update steps in a fixed point iteration to improve the convergence properties of the sequence. Despite being successfully used for many years to improve nonlinear solver behavior on a wide variety of problems, a theory that explains the often-observed accelerated convergence was lacking. In this talk, we give an introduction to AA, then present a proof of AA convergence which shows that it improves the linear convergence rate based on a gain factor of an underlying optimization problem, but also introduces higher order terms in the residual error bound. We then discuss improvements to AA based on our convergence theory, and show numerical results for the algorithms applied to several application problems including Navier--Stokes, Boussinesq, and nonlinear Helmholtz systems.

Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de

Host
WIAS Berlin
Wednesday, 17.03.2021, 11:30 (Online Event)
Seminar Interacting Random Systems
Daniel Heydecker, University of Cambridge, GB:
Large deviations of Kac's elastic particle system (online talk)
more ... Location
Online Event

Abstract
We consider Kac's stochastic model for a N-particle gas, with particles interacting by elastic collisions, and study the large deviations in the limit $Ntoinfty$ in the weak topology. There is a very natural candidate rate function, first proposed by Léonard, which amounts to the dynamic entropy of a flux measure plus an initial cost; with this rate function, we sketch the proof of an upper bound, and a lower bound restricted to a class of `sufficiently goods' paths. Perhaps surprisingly, we will see that the proposed rate function does not capture all of the possible large deviation behaviour. Lu and Wennberg showed that, even though the microscopic collisions preserve energy, there are solutions to the Boltzmann equation for which the energy is increasing, and these paths have 0 dynamic entropy. We will show that such paths can arise as large deviation limits with finite exponential cost, so cannot be excluded from large deviation analysis, but occur strictly more rarely than predicted by the rate function. At the level of the particle system, this occurs when a macroscopic proportion of the energy concentrates in $o(N)$ particles, which can happen with probability $e^-O(N)$.

Further Informations
Seminar Interacting Random Systems (Online Event)

Host
WIAS Berlin
Tuesday, 16.03.2021, 15:00 (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Kostas Papafitsoros, WIAS Berlin:
Optimization with learning-informed differential equation constraints and its applications (online talk)
more ... Location
Online Event

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Tuesday, 16.03.2021, 13:30 (Online Event)
Seminar Numerische Mathematik
Dr. Jürgen Fuhrmann, WIAS Berlin:
PDELib.jl: Towards software components for the numerical solution of partial differential equations in Julia
more ... Location
Online Event

Abstract
In recent years, in particular since the release of version 1.0, the Julia programming language gained significant momentum in fields related to scientific computing and data science. Taking advantage of accumulated experience and know-how in language design, designed around the just-in-time compilation paradigm, and featuring first class multidimensional array handling, it allows for the implementation of complex numerical algorithms without sacrificing efficiency. In recent years, in particular since the release of version 1..0, the Julia programming language gained significant momentum in fields related to scientific computing and data science.
In the talk, we will give a short overview on features of the Julia language which renders it well suited for the implementation of solvers for complex systems of partial differential equations, including multiple dispatch allowing for the implementation of automatic differentiation, interface oriented API design and its package manager supporting reusability and reproducibility.
We will report on the successful steps towards the implementation of software components for the numerical solution of PDEs.. Focus will be on the package VoronoiFVM.jl and supporting packages.

Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de

Host
WIAS Berlin
Tuesday, 09.03.2021, 15:00 (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Caroline Geiersbach, WIAS Berlin:
Stochastic approximation with applications to PDE-constrained optimization under uncertainty (online talk)
more ... Location
Online Event

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Wednesday, 03.03.2021, 11:30 (Online Event)
Seminar Interacting Random Systems
Cecile Mailler, The University of Bath, GB:
The ants walk: finding geodesics in graphs using reinforcement learning
more ... Location
Online Event

Abstract
How does a colony of ants find the shortest path between its nest and a source of food without any means of communication other than the pheromones each ant leave behind itself? In this joint work with Daniel Kious (Bath) and Bruno Schapira (Marseille), we introduce a new probabilistic model for this phenomenon. In this model, the nest and the source of food are two marked nodes in a finite graph. Ants perform successive random walks from the nest to the food, and ths distribution of the n-th walk depends on the trajectories of the (n-1) previous walks through some linear reinforcement mechanism. Using stochastic approximation methods, couplings with Pólya urns, and the electric conductances method for random walks on graphs, we prove that, in this model, the ants indeed eventually find the shortest path(s) between their nest and the source food.

Further Informations
Seminar Interacting Random Systems (Online Event)

Host
WIAS Berlin
Tuesday, 02.03.2021, 15:00 (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Yunfei Huang, Ludwig-Maximilians-Universität München:
Advanced data analysis for traction force microscopy and data-driven discovery of physical equations (online talk)
more ... Location
Online Event

Abstract
The plummeting cost of collecting and storing data and the increasingly available computational power in the last decade have led to the emergence of new data analysis approaches in various scientific fields. Frequently, the new statistical methodology is employed for analyzing data involving incomplete or unknown information. In this thesis, new statistical approaches are developed for improving the accuracy of traction force microscopy (TFM) and data-driven discovery of physical equations. TFM is a versatile method for the reconstruction of a spatial image of the traction forces exerted by cells on elastic gel substrates. The traction force field is calculated from a linear mechanical model connecting the measured substrate displacements with the sought-for cell-generated stresses in real or Fourier space, which is an inverse and ill-posed problem. This inverse problem is commonly solved making use of regularization methods. Here, we systematically test the performance of new regularization methods and Bayesian inference for quantifying the parameter uncertainty in TFM. We compare two classical schemes, L1- and L2-regularization with three previously untested schemes, namely Elastic Net regularization, Proximal Gradient Lasso, and Proximal Gradient Elastic Net. We find that Elastic Net regularization, which combines L1 and L2 regularization, outperforms all other methods with regard to accuracy of traction reconstruction. Next, we develop two methods, Bayesian L2 regularization and Advanced Bayesian L2 regularization, for automatic, optimal L2 regularization.. We further combine the Bayesian L2 regularization with the computational speed of Fast Fourier Transform algorithms to develop a fully automated method for noise reduction and robust, standardized traction-force reconstruction that we call Bayesian Fourier transform traction cytometry (BFTTC). This method is made freely available as a software package with graphical user-interface for intuitive usage. Using synthetic data and experimental data, we show that these Bayesian methods enable robust reconstruction of traction without requiring a difficult selection of regularization parameters specifically for each data set. Next, we employ our methodology developed for the solution of inverse problems for automated, data-driven discovery of ordinary differential equations (ODEs), partial differential equations (PDEs), and stochastic differential equations (SDEs). To find the equations governing a measured time-dependent process, we construct dictionaries of non-linear candidate equations. These candidate equations are evaluated using the measured data. With this approach, one can construct a likelihood function for the candidate equations. Optimization yields a linear, inverse problem which is to be solved under a sparsity constraint. We combine Bayesian compressive sensing using Laplace priors with automated thresholding to develop a new approach, namely automatic threshold sparse Bayesian learning (ATSBL). ATSBL is a robust method to identify ODEs, PDEs, and SDEs involving Gaussian noise, which is also referred to as type I noise. We extensively test the method with synthetic datasets describing physical processes. For SDEs, we combine data-driven inference using ATSBL with a novel entropy-based heuristic for discarding data points with high uncertainty. Finally, we develop an automatic iterative sampling optimization technique akin to Umbrella sampling. Therewith, we demonstrate that data-driven inference of SDEs can be substantially improved through feedback during the inference process if the stochastic process under investigation can be manipulated either experimentally or in simulations.

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Friday, 26.02.2021, 13:00 (Online Event)
AA2 - Materials, Light, Devices
Dr. Manuel Landstorfer, WIAS Berlin:
Modeling of concentration and electric field dependent susceptibilities in electrolytes (online talk)
more ... Location
Online Event

Host
Freie Universität Berlin
Humboldt-Universität zu Berlin
WIAS Berlin
Thursday, 25.02.2021, 14:00 (Online Event)
Seminar Numerische Mathematik
Vojtěch Miloš, University of Chemistry and Technology Technická, Prag; Petr Vágner, WIAS Berlin:
Modelling of YSZ|LSM|O_2 electrode with experimental validation
more ... Location
Online Event

Abstract
A generalized Poisson-Nernst-Planck model of an yttria-stabilized zirconia (YSZ) electrolyte endowed with a lanthanum strontium manganite (LSM)--oxygen electrode interface is formulated with in the framework of non-equilibrium thermodynamics. The model takes into account limitations in oxide ion concentrations due to the limited availability of oxygen vacancies. The electrolyte model is coupled with a general reaction kinetic scheme capturing the oxygen reduction.
The model is fitted and compared to a large experimental dataset of electrochemical impedance spectra and cyclic voltammograms spanning temperatures from 700$^circ$ C to 850$^circ$ C. An apriori temperature dependenciies of the model parameters are introduced and the Nelder-Mead algorithm is employed to minimize a compound cost function. The compound cost function allows for different weights if the two types of experiments leading to interesting physical interpretations.

Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de

Host
WIAS Berlin
Wednesday, 24.02.2021, 10:00 (Online Event)
Forschungsseminar Mathematische Statistik
Prof. Dr. Torsten Hothorn, Universität Zürich, Switzerland:
Understanding and applying transformation models (online talk)
more ... Location
Online Event

Abstract
The mlt package implements maximum likelihood estimation in the class of conditional transformation models. Based on a suitable explicit parameterization of the unconditional or conditional transformation function using infrastructure from package basefun, we show how one can define, estimate, and compare a cascade of increasingly complex transformation models in the maximum likelihood framework. Models for the unconditional or conditional distribution function of any univariate response variable are set up and estimated in the same computational framework simply by choosing an appropriate transformation function and parameterization thereof. As it is computationally cheap to evaluate the distribution function, models can be estimated by maximization of the exact likelihood, especially in the presence of random censoring or truncation. The relatively dense high-level implementation in the R system for statistical computing allows generalization of many established implementations of linear transformation models, such as the Cox model or other parametric models for the analysis of survival or ordered categorical data, to the more complex situations illustrated in this talk.

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 23.02.2021, 15:15 (Online Event)
Oberseminar Nonlinear Dynamics
Prof. Dr. Alexandre Nolasco de Carvalho, University of São Paulo at São Carlos:
Gradient non-autonomous dynamics
more ... Location
Online Event

Abstract
In this lecture we present our approach for the study of the asymptotics of autonomous and non-autonomous dynamical systems. This unified approach shows how some different notions of attractors play a role in the description of the dynamics and enable us to address the gradient structure within non-autonomous attractors. As an application we characterize the gradient structure within the uniform attractor for a non-autonomous Chafee-Infante problem. A few, in our view, interesting and challenging problems, for future studies, are presented at the end of the lecture.

Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/82815629022.

Host
Freie Universität Berlin
WIAS Berlin
Tuesday, 23.02.2021, 15:00 (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Priv.-Doz. Dr. Christian Bayer, WIAS Berlin:
A pricing BSPDE for rough volatility (online talk)
more ... Location
Online Event

Abstract
In this talk, we study the option pricing problems for rough volatility models. As the framework is non-Markovian, the value function for a European option is not deterministic; rather, it is random and satisfies a backward stochastic partial differential equation (BSPDE). The existence and uniqueness of weak solution is proved for general nonlinear BSPDEs with unbounded random leading coefficients whose connections with certain forward-backward stochastic differential equations are derived as well. These BSPDEs are then used to approximate American option prices. A deep leaning-based method is also investigated for the numerical approximations to such BSPDEs and associated non-Markovian pricing problems. Finally, the examples of rough Bergomi type are numerically computed for both European and American options.

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Tuesday, 23.02.2021, 10:15 (Online Event)
Seminar Nichtlineare Optimierung und Inverse Probleme
Thomas Nagel, Technische Universität Berlin:
Surface detection of clouds by using simple artificial neural networks
more ... Location
Online Event

Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/98493865627.

Host
WIAS Berlin
Thursday, 18.02.2021, 14:00 (Online Event)
Seminar Numerische Mathematik
Derk Frerichs, WIAS Berlin:
On reducing spurious oscillations in discontinuous Galerkin methods for convection-diffusion equations
more ... Location
Online Event

Abstract
Among other desirable features, standard discontinuous Galerkin methods for discretizing steady-state convection-diffusion-reaction equations are able to produce sharp layers in the convection-dominated regime, but also show large spurious oscillations. A computationally cheap way to reduce nonphysical oscillations is to apply post-processing techniques that replace the solution in the vicinity of layers by linear or constant approximations. This talk presents known post-processing methods form the literature, and proposes several generalizations as well as novel modifications. Results for two numerical benchmark problems are shown indicating pros and cons of the methods.

Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de

Host
WIAS Berlin
Wednesday, 17.02.2021, 15:15 (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Giovanni P. Galdi, University of Pittsburgh, USA:
On the self-propelled motion of a rigid body in a viscous liquid by time-periodic boundary data (online talk)
more ... Location
Online Event

Abstract
Consider a rigid body, B, constrained to move by translational motion in an unbounded viscous liquid. The driving mechanism is a given distribution of time-periodic velocity field, v, at the interface body-liquid, of magnitude  (in appropriate function class). The main objective is to find conditions on v ensuring that B performs a non-zero net motion, namely, B can cover any given distance in a finite time. This study is mostly motivated by the self-propulsion of vibrating bodies in viscous liquids, where the vibration is generated by the oscillation of an internal mass. We show that the approach to the problem depends on whether the averaged value of v over a period of time is (case (b)) or is not (case (a)) identically zero. In case (a) we solve the problem in a relatively straightforward way, by showing that, for small , it reduces to the study of a suitable and well-investigated time-independent Stokes (linear) problem. In case (b), however, the question is much more complicated, because we show that it cannot be brought to the study of a linear problem. Therefore, in case (b), self-propulsion is a genuinely nonlinear issue that we solve directly on the nonlinear system by a contradiction argument. In this way, we are able to give, also in case (b), sufficient conditions for self-propulsion (for small ). Finally, we demonstrate, by means of counterexamples, that such conditions are, in general, also necessary.

Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Wednesday, 17.02.2021, 11:30 (Online Event)
Seminar Interacting Random Systems
Thorsten Lucke, Technische Universität Berlin:
Influence of mobility on telecommunication networks --- some thoughts (online talk)
more ... Location
Online Event

Abstract
The Boolean model provides a nice framework for describing ad-hoc networks. It is well known that under certain assumptions on the distribution of the radii and the intensity of the Poisson process we can observe critical phenomena such as percolation or global connectivity. However, if we start in a subcritical regime, i.e., the intensity is below a critical threshold, can we manipulate the connectivity properties, if we allow the participants to move? This talk will provide a brief introduction to mobility models such as the random waypoint model.

Further Informations
Seminar Interacting Random Systems (Online Event)

Host
WIAS Berlin
Wednesday, 17.02.2021, 10:00 (Online Event)
Forschungsseminar Mathematische Statistik
Georg Keilbar, Humboldt-Universität zu Berlin:
Finite sample bounds for quantiles using SGD (online talk)
more ... Location
Online Event

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 16.02.2021, 15:00 (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Alexandre Pannier, Imperial College London , UK:
Large and moderate deviations for stochastic Volterra systems (online talk)
more ... Location
Online Event

Abstract
We provide a unified treatment of pathwise large and moderate deviations principles for a general class of multidimensional stochastic Volterra equations with singular kernels, not necessarily of convolution form. Our methodology is based on the weak convergence approach by Budhiraja, Dupuis and Ellis. We show in particular how this framework encompasses most rough volatility models used in mathematical finance, yields pathwise moderate deviations for the first time and generalises many recent results in the literature. This is joint work with Antoine Jacquier.

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Friday, 12.02.2021, 13:00 (Online Event)
AA2 - Materials, Light, Devices
Dr. Benjamin Jurgelucks, Humboldt-Universität zu Berlin:
Material parameter identification and sensitivity optimization for piezoelectric ceramics (online talk)
more ... Location
Online Event

Abstract
Recent material parameter identification methods for piezoelectric ceramics rely on the solution of an inverse problem with the electrical impedance as the measurable quantity. A common complaint is that the sensitivity of impedance with respect to some material parameters is small or zero. Thus, some material parameters cannot be identified reliably. However, the sensitivity of impedance can be increased with the help of Algorithmic Differentiation by optimizing the shape of the electrodes attached to the ceramic. This greatly improves the accuracy of current material parameter identification methods for piezoelectrics. Furthermore, based on pre-optimized electrode shapes one can even achieve arbitrary sensitivity.

Further Informations
AA2 - Materials, Light, Devices

Host
Humboldt-Universität zu Berlin
Technische Universität Berlin
WIAS Berlin
Thursday, 11.02.2021, 14:00 (Online Event)
Seminar Numerische Mathematik
Dr. Ulrich Wilbrandt, WIAS Berlin:
Optimization of stabilization parameters for convection-dominated convection-diffusion equations
more ... Location
Online Event

Abstract
Solutions to convection-dominated convection-diffusion equations typically have spurious oscillations and other non-physical properties. To overcome these difficulties in the Finite Element context one often uses stabilizations, which are additional terms in the weak formulation. We will consider the streamline upwind Petrov-Galerkin (SUPG) and a spurious oscillations at layers diminishing (SOLD) method. These involve a user-chosen parameter on each cell and it is unknown how to choose these parameters exactly. The approach presented in this talk is to let an optimization algorithm decide on these parameters which leaves the choice of an appropriate objective to the user. We will show some objectives and their motivation and discuss a reduction of the rather larger control space.

Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de

Host
WIAS Berlin
Wednesday, 10.02.2021, 10:00 (Online Event)
Forschungsseminar Mathematische Statistik
Dr. Eftychia Solea, École Nationale de la Statistique et de l'Analyse de l'Information (ENSAI), France:
Nonparametric and high-dimensional functional graphical models (online talk)
more ... Location
Online Event

Abstract
We consider the problem of constructing nonparametric undirected graphical models for high-dimensional functional data. Most existing statistical methods in this context assume either a Gaussian distribution on the vertices or linear conditional means. In this article we provide a more flexible model which relaxes the linearity assumption by replacing it by an arbitrary additive form. The use of functional principal components offers an estimation strategy that uses a group lasso penalty to estimate the relevant edges of the graph. We establish concentration inequalities for the resulting estimators allowing both the number of predictors and the number of functional principal components to diverge to infinity with increasing sample size. We also investigate the empirical performance of our method through simulation studies and a real data application.

Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 09.02.2021, 15:15 (Online Event)
Oberseminar Nonlinear Dynamics
Svetlana Gurevich, Westfälische Wilhelms-Universit&