Applied Math Seminar

Abstract: Modern machine learning and scientific computing pose optimization challenges of unprecedented scale and complexity, demanding fundamental advances in both theory and algorithmic design for nonconvex optimization. This talk presents recent advances that address these challenges by exploiting matrix and tensor structures, integrating adaptivity, and leveraging sampling techniques. In the first part, I introduce AdaGO, […]

Abstract: The talk introduces a conjecture on the first exit time of fractional Brownian motion: the upper-tail probability for a fractional Brownian motion to first exit a positive-valued barrier over time […]

Abstract: A proper coloring of a graph is an assignment of colors from \( \{1, 2, \ldots, k\} \) to each node of a graph such that no two nodes […]

Abstract: Existing tools for explaining complex models and systems are associational rather than causal and do not provide mechanistic understanding. We propose a new notion called counterfactual explainability for causal attribution that is motivated by the concept of genetic heritability in twin studies. Counterfactual explainability extends methods for global sensitivity analysis (including the functional analysis […]

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 […]

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 […]

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 […]

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 eigenvalue over admissible densities satisfying pointwise bounds and a fixed integral constraint. We establish the existence of optimal solutions and provide structural characterizations: minimizers are […]

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 a great achievement of the human intellect that we are able to locate fundamental mechanisms shared by phenomenon with such a dramatic difference in scale […]

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 inference time, without any weight updates. ICON acts as a few-shot learner across forward and inverse problems for ODEs, PDEs, and mean-field control. I will […]