Upcoming Events
- Wednesday, 17.07.2024, 14:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Daniel Matthes, Technische Universität München:
Covariance modulated optimal transport: Geometry and gradient flows
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
This talk is about a novel variant of optimal mass transport in which particles move with a global linear but anisotropic mobility depending on the covariance of the ensemble density. This gives rise to a novel kind of Wasserstein metric that provides a rigorous gradient flow formulation of the mean-field limit for the ensemble Kalman sampling. In combination with the abstract machinery of metric gradient flows, the new metric is an effective tool to study the rate of convergence of these methods. I shall present several analytic results about the modulated Wasserstein metric. The first is the splitting representation, which allows to write the modulated metric as the sum of two simpler metrics, one measuring the distance in terms of first and second moments, the other one measuring in terms of shapes. The second result is about geodesic convexity and the related rates of convergence in gradient flows. Specifically, we prove exponential equilibration in linear Fokker-Planck equations with Gaussian steady states at a rate that does not depend on the covariance of the Gaussian. The third and only partial result is about geodesics, that we prove to exist for sufficiently close densities, or densities with multiple reflection symmetries. We also characterize geodesics in terms of particle trajectories, that are no longer straight line as in the genuine Wasserstein metric, but follow more complicated curves that satisfy second order ordinary differential equations. This is joint work with Andre Schlichting, Matthias Erbar, Franca Hoffmann, and Martin Burger.
Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Thursday, 18.07.2024, 10:00 (Berlin Mitte)
- MATH+ Thematic Einstein Semester on “Mathematics for Quantum Technologies”
Prof. Ulf Leonhardt, Weizmann Institute of Science, Israel:
Third advanced lecture of the series “Forces of the quantum vacuum” .
more ... Location
Berlin Mitte
Abstract
Topic: Applications
Imaginary frequencies for capturing the broad band of quantum forces
Thermal Casimir effect
Perfectly conducting cavity
Magnetic mirror and Casimir repulsion
Permittivity hierarchy and repulsive Casimir forces
Negative refraction and quantum levitation
Engineering in the imaginary part of the spectrum
Host
WIAS Berlin
Einstein Foundation Berlin
- Thursday, 18.07.2024, 15:00 (WIAS-406)
- Seminar Materialmodellierung
Prof. Dr. Jan Giesselmann, Technische Universität Darmstadt:
A posteriori error estimates for systems of hyperbolic conservation laws modeling compressible flows
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Abstract
Hyperbolic conservation laws are a class of PDEs that have many applications, most notably in compressible fluid flows when viscosity is neglected. While these equations are successfully used by engineers in simulations, there are many open questions regarding their mathematical study. These are mostly driven by to the non-uniqueness of entropy solutions in multiple space dimensions but even in one space dimensions stability of solutions is challenging if one is to go beyond initial data that are small in BV.
The challenges in the mathematical analysis have lead to a situation where a variety of sophisticated numerical schemes exists and is successfully used in practice but the mathematical foundations of these methods are not as substantial as one would hope. This issue has been addressed by several authors in recent years and we plan plan to present what has been achieved in the field of a posteriori error estimates, i.e. explicit bounds for the error of the numerical solution that can be computed from the numerical solution.
A fundamental building block of a posteriori error estimates are stability theories that allow to relate certain norms of residuals, i.e. quantities measuring by how much an approximate solution fails to satisfy the PDE, to certain norms of the error, i.e. the difference between numerical and exact solution. Examples of such stability theories include the classical relative entropy framework, the theory of shifts developed by Vasseur and coworkers and recent results by Bressan and coworkers.
We will describe these stability results and discuss how they have been used to derive a posteriori error estimates for hyperbolic conservation laws.
Further Informations
Seminar Materialmodellierung
Host
WIAS Berlin
- Friday, 19.07.2024, 10:00 (Berlin Mitte)
- MATH+ Thematic Einstein Semester on “Mathematics for Quantum Technologies”
Prof. Ulf Leonhardt, Weizmann Institute of Science, Israel:
Fourth advanced lecture of the series “Forces of the quantum vacuum” .
more ... Location
Berlin Mitte
Abstract
Topic: Outlook
The quantum vacuum seen by accelerated observers (relativistic acceleration, Rindler coordinates, Unruh effect)
Entanglement in the quantum vacuum
Classical analogue of the Unruh effect
The case for a Casimir cosmology
Host
WIAS Berlin
Einstein Foundation Berlin
- Tuesday, 23.07.2024, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Yuanyuan Li, Fudan University, China, Volksrepublik:
Function and derivative approximation by shallow neural networks
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
We investigate a Tikhonov regularization scheme specifically tailored for shallow neural networks within the context of solving a classic inverse problem: approximating an unknown function and its derivatives within a bounded domain based on noisy measurements. The proposed Tikhonov regularization scheme incorporates a penalty term that takes three distinct yet intricately related network (semi)norms: the extended Barron norm, the variation norm, and the Radon-BV seminorm. These choices of the penalty term are contingent upon the specific architecture of the neural network being utilized. We establish the connection between various network norms and particularly trace the dependence of the dimensionality index, aiming to deepen our understanding of how these norms interplay with each other. We revisit the universality of function approximation through various norms, establish rigorous error-bound analysis for the Tikhonov regularization scheme, and explicitly elucidate the dependency of the dimensionality index, providing a clearer understanding of how the dimensionality affects the approximation performance.
Further Informations
Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Wednesday, 24.07.2024, 14:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Emil Wiedemann, Friedrich-Alexander-Universität Erlangen-Nürnberg:
Measure-valued solutions in fluid dynamics
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
As more and more ill-posedness results have been shown for fluid PDEs (not only by convex integration!), the idea to solve the Cauchy problem by some unique weak or entropy solution has become questionable. Instead, non-deterministic solution concepts such as measure-valued or statistical have sparked much recent research interest. They also seem to be more in line with well-known theories of turbulence, which are typically statistical. I will give an overview of measure-valued solution concepts, including their weak-strong stability, their relation to more conventional solutions, and questions of existence. Links to other notions of "very weak" solution (dissipative, subsolutions, energy-variational) will briefly be discussed.
Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 30.07.2024, 15:00 (WIAS-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Egor Gladin, Humboldt Universität zu Berlin:
Cutting plane methods and dual problems
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Abstract
The present talk examines cutting plane methods, which are a group of iterative algorithms for minimizing a (possibly nonsmooth) convex function over a compact convex set. We consider two prominent examples, namely, the ellipsoid method and Vaidya's method, and show that their convergence rate is preserved even when an inexact oracle is used. Furthermore, we demonstrate that it is possible to use these methods in the context of stochastic optimization efficiently. Another direction where cutting plane methods can be useful is Lagrange dual problems. Commonly, the objective and its derivatives can only be computed approximately in such problems. Thus, the methods' insensitivity to error in subgradients comes in handy. As an application example, we propose a linearly converging dual method for a constrained Markov decision process (CMDP) based on Vaidya's algorithm with an inexact oracle. The talk also discusses the concept of accuracy certificates for convex minimization problems. Certificates allow for online verification of the accuracy of approximate solutions and provide a theoretically valid online stopping criterion. We generalize the notion of accuracy certificates for the setting of an inexact first-order oracle. In particular, this includes the setting of a dual problem where the dual function and its derivatives don't necessarily have closed-form representations. Furthermore, we propose an explicit way to construct accuracy certificates for a large class of cutting plane methods that use polytopes as localizers.
Further Informations
Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Thursday, 08.08.2024, 13:30 (WIAS-406)
- Seminar Materialmodellierung
Dr. Ferran Brosa Planella, University of Warwick, GB:
Asymptotic methods for lithium-ion battery models
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Abstract
Lithium-ion batteries have become ubiquitous over the past decade, and they are called to play even a more important role with the electrification of vehicles. In order to design better and safer batteries and to manage them more efficiently, we need models than can predict the battery behaviour accurately and fast. However, in many cases these models are still posed in an ad hoc way, which makes them hard to extend and may lead to inconsistencies. In this talk we will see some examples on how asymptotic methods can be applied to obtain simple models that can be used in battery control and parameterisation.
Host
WIAS Berlin
- Thursday, 05.09.2024, 12:00 (WIAS-405-406)
- Seminar Interacting Random Systems
Martijn Gösgens, TU Eindhoven:
tba
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
tba
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Wednesday, 18.09.2024, 10:00 (WIAS-405-406)
- Seminar Numerische Mathematik
Albert Pool, DLR:
Nonlinear dynamics as a ground-state solution on quantum computers
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Host
WIAS Berlin
- Wednesday, 18.09.2024, 10:00 (WIAS-405-406)
- Seminar Numerische Mathematik
Albert J. Pool, Deutsches Zentrum für Luft- und Raumfahrt e.V.:
Nonlinear dynamics as a ground-state solution on quantum computers
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
For the solution of time-dependent nonlinear differential equations, we present variational quantum algorithms (VQAs) that encode both space and time in qubit registers. The spacetime encoding enables us to obtain the entire time evolution from a single ground-state computation. We describe a general procedure to construct efficient quantum circuits for the cost function evaluation required by VQAs. To mitigate the barren plateau problem during the optimization, we propose an adaptive multigrid strategy. The approach is illustrated for the nonlinear Burgers equation. We classically optimize quantum circuits to represent the desired ground-state solutions, run them on IBM Q System One and Quantinuum System Model H1, and demonstrate that current quantum computers are capable of accurately reproducing the exact results.
Host
WIAS Berlin