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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