Veranstaltungen
- Dienstag, 12.12.2023, 13:30 Uhr (WIAS-ESH)
- Seminar Numerische Mathematik
Jan Philipp Thiele, WIAS Berlin:
Error-controlled space-time finite elements, algorithms and implementations for nonstationary problems
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
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.
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Numerics Seminar (FG3+LG5)
Veranstalter
WIAS Berlin
- Dienstag, 12.12.2023, 15:00 Uhr (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
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Abstrakt
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.
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Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715
Veranstalter
WIAS Berlin
- Mittwoch, 13.12.2023, 10:00 Uhr (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Dr. Boris Buchmann, Australian National University, Australien:
Weak subordination of multivariate Levy processes (hybrid talk)
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
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)
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Der Vortrag findet auch via Zoom statt: https://zoom.us/j/159082384
Veranstalter
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Mittwoch, 13.12.2023, 11:30 Uhr (WIAS-405-406)
- Seminar Interacting Random Systems
Beatriz Salvador, Technical University of Lisbon:
From duality to correlations: Application to the partial exclusion process SEP(alpha)
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstrakt
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.
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Seminar Interacting Random Systems (Hybrid Event)
Veranstalter
WIAS Berlin
- Mittwoch, 13.12.2023, 14:15 Uhr (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Juergen Sprekels, WIAS Berlin:
Necessary and sufficient optimality conditions in the sparse optimal control of singular Allen--Cahn systems with dynamic boundary conditions
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
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Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
- Donnerstag, 14.12.2023, 14:00 Uhr (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
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
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.
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Numerics Seminar (FG3+LG5)
Veranstalter
WIAS Berlin
- Donnerstag, 14.12.2023, 16:00 Uhr (WIAS-ESH)
- Forschungsseminar Mathematische Modelle der Photonik
Robert Finn, Tyndall National Institute:
UV light emitters: from alloy microstructure to carrier transport
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Veranstalter
WIAS Berlin
- Freitag, 15.12.2023, 10:00 Uhr (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Prof. Dr. Laura Sangalli, Politecnico di Milano, Italien:
Physics-informed spatial and functional data analysis
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
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.
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Der Vortrag findet auch via Zoom statt: https://zoom.us/j/159082384
Veranstalter
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Dienstag, 19.12.2023, 10:15 Uhr (WIAS-406)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Mathias Oster, RWTH Aachen:
Going deep with dictionaries: ODE-based models
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Veranstalter
WIAS Berlin
- Dienstag, 19.12.2023, 14:00 Uhr (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
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
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
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Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations
Veranstalter
WIAS Berlin
- Dienstag, 19.12.2023, 15:00 Uhr (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 (hybrid talk)
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Abstrakt
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.
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Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715
Veranstalter
WIAS Berlin
- Mittwoch, 20.12.2023, 14:15 Uhr (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Georg Heinze, WIAS Berlin:
Graph-based nonlocal gradient flows and their local limits
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
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.
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Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
- Mittwoch, 10.01.2024, 11:30 Uhr (WIAS-405-406)
- Seminar Interacting Random Systems
Wolfgang König, WIAS Berlin:
A PhD project on dormancy in population dynamics in random environment (Part II)
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
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Seminar Interacting Random Systems (Hybrid Event)
Veranstalter
WIAS Berlin
- Dienstag, 23.01.2024, 15:00 Uhr (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Luca Pelizzari, WIAS Berlin:
Rough PDEs for local stochastic volatility models (hybrid talk)
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstrakt
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.
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Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715
Veranstalter
WIAS Berlin
- Mittwoch, 24.01.2024, 14:15 Uhr (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Anastasija Pešić, Humboldt-Universität zu Berlin:
Variational models for pattern formation in biomembranes
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
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.
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Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)
Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin