Upcoming Events

Wednesday, 19.03.2025, 11:30 (WIAS-405-406)

Seminar Interacting Random Systems
César Zarco-Romero:
The stacks picture of a uniform spanning tree
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
In contrast to Wilson's algorithm, the Stacks picture is a less known notion for efficiently generating a spanning tree at random in a connected graph. We revisit both tools related to loop-erased random walks. For ease of presentation, we restrict our attention to two dimensions for the infinite case. We will also mention a couple of points of intersection in other areas in Probability where research is being developed.

Host
WIAS Berlin

March 26 – 28, 2025 (IOW)

Workshop/Konferenz: Leibniz MMS Days 2025
more ... Location
Leibniz Institute for Baltic Sea Research Warnemünde (IOW).

Host
Leibniz Institute for Baltic Sea Research Warnemünde (IOW)
WIAS Berlin

Thursday, 27.03.2025, 14:00 (WIAS-405-406)

Seminar Numerische Mathematik
Prof. Cornelis Vuik, Delft University of Technology:
Resolving divergence: the first multigrid scheme for the highly indefinite Helmholtz equation using classical components
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
In this talk, we (V. Dwarka and C. Vuik) present the first stand-alone classical multigrid solver for the highly in- definite 2D Helmholtz equation with constant costs per iteration, addressing a longstanding open problem in numerical analysis [1]. Our work covers both large constant and non- constant wavenumbers up to k = 500 in 2D. We obtain a full V - and W -cycle without any level-dependent restrictions. Another powerful feature is that it can be combined with the computationally cheap weighted Jacobi smoother. The key novelty lies in the use of higher-order inter-grid transfer operators [2]. When combined with coarsening on the Complex Shifted Laplacian, rather than the original Helmholtz operator, our solver is h-independent and scales linearly with the wavenumber k. If we use GMRES(3) smoothing we obtain k- independent convergence, and can coarsen on the original Helmholtz operator, as long as the higher-order transfer operators are used. This work opens doors to study robustness of contemporary solvers, such as machine learning solvers inspired by multigrid components, without adding to the black-box complexity.

Host
WIAS Berlin

Tuesday, 01.04.2025, 15:00 (WIAS-406)

Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Prof. Dr. Vladimir Spokoiny, WIAS Berlin:
Estimation and inference for deep neuronal network: Blessing of dimension
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
Nonlinear regression problem is one of the most popular and important statistical tasks. The first methods like nonlinear least squares estimation go back to Gauss and Legendre. Recent developments in statistics and machine learning like Deep Neuronal Networks (DNN) or nonlinear PDE stimulate new research in this direction which has to address the important issues and challenges of statistical inference such as huge complexity and parameter dimension of the model, limited sample size, lack of convexity and identifiability, among many others. Classical results of nonparametric statistics in terms of rate of convergence do not really address the mentioned issues. This paper offers a general approach to studying a nonlinear regression problem based on the notion of effective dimension. Despite generality, all the presented bounds are nearly sharp and the classical asymptotic results can be obtained as simple corollaries. In applications to DNN, the proposed approach helps to rigorously address the mentioned issues of overparametrization, non-convex optimization, and lack of identifiability.

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

Host
WIAS Berlin

Wednesday, 30.04.2025, 14:15 (WIAS-ESH)

Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Rossella Giorgio, Technische Universität Wien, Österreich:
Nonlocal analysis of energies in micromagnetics
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In this talk we provide conditions in order to formally justify a nonlocal analysis of energies in Micromagnetics. Specifically, we first consider a nonlocalto-local approximation of exchange energy functionals, extending the wellknown Bourgain--Brezis--Mironescu formula to encompass the scenario where antisymmetric contributions are encoded. The key points are a pointwise convergence result and a Gamma-convergence argument. After the nonlocal approximation, we investigate the existence and qualitative properties of minimizers, focusing on the competition between a nonlocal symmetric exchange interaction, which penalizes spatial variations in magnetization, and a magnetostatic self-energy term that accounts for long-range dipolar interactions. For spherical domains, we generalize Brown's fundamental results by identifying critical radii such that uniform magnetizations are preferable for the small-body regime, while non-uniform magnetization configurations become dominant in the large-body regime. This is joint work with E. Davoli, G. Di Fratta and L. Lombardini.

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

Host
Humboldt-Universität zu Berlin
WIAS Berlin