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 […]

Abstract: We study the optimization of Steklov eigenvalues with respect to a boundary density function ρ on a bounded Lipschitz domain. We investigate the minimization and maximization of a Steklov […]

Abstract: Turbulence influences our lives in a multitude of ways, ranging from the mundane (when we stir milk into our coffee) to the spectacular (the formation of galaxies). It is […]

Abstract: I will introduce In-Context Operator Networks (ICON), a framework in which a single neural network learns solution operators for differential equations directly from a few prompted input-output examples at […]

In multi-armed trials, adaptive designs are a popular way to increase estimation efficiency or identify optimal treatments. Many recent papers have proposed adaptive methods for minimizing the error of unbiased estimators that consider each treatment arm in isolation. This approach may be inefficient, because it fails to borrow shared information across the treatment arms. We […]

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Political scientists forecast elections, not primarily to satisfy public interest, but to validate statistical models used for estimating quantities of scholarly interest. Although scholars have learned a great deal from […]

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