Veranstaltungen

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Dienstag, 07.02.2023, 15:00 Uhr (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)
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstrakt
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.

Weitere Informationen
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

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

Abstrakt
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.

Weitere Informationen
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Veranstalter
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Mittwoch, 08.02.2023, 11:30 Uhr (WIAS-405-406)
Seminar Interacting Random Systems
Dave Jacobi, TU Berlin:
Super-Brownian motion with dormancy
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstrakt
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.

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Seminar Interacting Random Systems (Hybrid Event)

Veranstalter
WIAS Berlin
Mittwoch, 08.02.2023, 15:15 Uhr (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)
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
Please see here.

Weitere Informationen
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.

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
Montag, 13.02.2023, 10:30 Uhr (WIAS-405-406)
Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Dr.-Ing. Julia Kowal, Technische Universität Berlin:
Working principle and ageing of batteries
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Veranstalter
WIAS Berlin
Dienstag, 14.02.2023, 15:00 Uhr (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)
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstrakt
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).

Weitere Informationen
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

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

Weitere Informationen
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Veranstalter
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Mittwoch, 15.02.2023, 15:15 Uhr (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)
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
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.

Weitere Informationen
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.

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
Donnerstag, 16.02.2023, 14:00 Uhr (Online Event)
Seminar Nichtglatte Variationsprobleme und Operatorgleichungen
Dr. Christian Parkinson, University of Arizona, USA:
The Hamilton--Jacobi formulation of optimal path planning for autonomous vehicles (online talk)
mehr ... Veranstaltungsort
Online Event

Abstrakt
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.

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Seminar Nichtglatte Variationsprobleme und Operatorgleichungen

Veranstalter
WIAS Berlin
Mittwoch, 22.02.2023, 15:15 Uhr (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)
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
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.

Weitere Informationen
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.

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
Donnerstag, 23.02.2023, 11:30 Uhr (WIAS-405-406)
Seminar Interacting Random Systems
Élie de Panafieu, Nokia Bell Labs, Frankreich:
Active clustering of a set using pairwise comparisons
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstrakt
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).

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Seminar Interacting Random Systems (Hybrid Event)

Veranstalter
WIAS Berlin
Mittwoch, 01.03.2023, 11:30 Uhr (WIAS-405-406)
Seminar Interacting Random Systems
Partha Gosh, TU Braunschweig:
tba
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Weitere Informationen
Seminar Interacting Random Systems (Hybrid Event)

Veranstalter
WIAS Berlin
Donnerstag, 09.03.2023, 14:00 Uhr (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)
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstrakt
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.

Weitere Informationen
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Veranstalter
WIAS Berlin
Mittwoch, 15.03.2023, 11:30 Uhr (WIAS-405-406)
Seminar Interacting Random Systems
Christof Külske, Ruhr-Universität Bochum:
tba
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Weitere Informationen
Seminar Interacting Random Systems (Hybrid Event)

Veranstalter
WIAS Berlin
Mittwoch, 22.03.2023, 10:00 Uhr (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
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstrakt
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.

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Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations

Veranstalter
WIAS Berlin
Mittwoch, 22.03.2023, 11:30 Uhr (WIAS-405-406)
Seminar Interacting Random Systems
Andreas Klippel, Technische Universität Darmstadt:
tba
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

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Seminar Interacting Random Systems (Hybrid Event)

Veranstalter
WIAS Berlin
Montag, 17.04.2023, 10:00 Uhr (ATB)
Leibniz MMS Days
Leibniz MMS Days 2023
mehr ... Veranstaltungsort
Agricultural Engineering and Bioeconomy Potsdam

Veranstalter
Leibniz Institute for Agricultural Engineering and Bioeconomy
WIAS Berlin
Freitag, 07.07.2023, 08:00 Uhr (Harnack-Haus)
Workshop: Phase transitions in random point systems
Phase transitions in random point systems
mehr ... Veranstaltungsort
Harnack-Haus -- Tagungsstätte der Max-Planck-Gesellschaft

Veranstalter
WIAS Berlin
DFG Schwerpunktprogramm 2265
Montag, 17.07.2023, 09:00 Uhr (Harnack-Haus)
SPP2265 Summer School: Probability and geometry on configuration spaces
SPP2265 Summer School: Probability and geometry on configuration spaces
mehr ... Veranstaltungsort
Harnack-Haus -- Tagungsstätte der Max-Planck-Gesellschaft

Veranstalter
WIAS Berlin
DFG Schwerpunktprogramm 2265