Applied Math Seminar

Abstract: We present a new approach for deriving structure-preserving numerical discretizations of Fokker-Planck equations by establishing a connection between the Fokker-Planck equation and its semi-discrete master equation at the level of the energy-dissipation law. We determine the transition rate in the master equation via the detailed balance condition and the spatial discretization of the continuous […]

Abstract: The Shapley value is a ubiquitous framework for attribution in machine learning, encompassing feature importance, data valuation, and causal inference. However, its exact computation is generally intractable, necessitating efficient approximation methods. While the most effective and popular estimators leverage the paired sampling heuristic to reduce estimation error, the theoretical mechanism driving this improvement has […]

Abstract: This talk presents a regularity criterion for the three-dimensional Navier–Stokes equations based on finitely many observations of the flow. Motivated by data assimilation, we study a nudging algorithm that incorporates coarse spatial measurements through general interpolation operators. We show that suitable conditions on the observed data guarantee global regularity of the associated system and […]

Abstract: In this talk, we will describe a well/ill-posedness result for the 2D incompressible Euler equations. We investigate solutions in a setting logarithmically smoother than previously done, in a hope to identify the key dynamics leading to a breakdown of regularity in 2D fluid flow. When order of the logarithmic derivative is sufficiently large one […]