Title: An optimal transport perspective on uncertainty quantification

Abstract: In many scientific areas, a deterministic model (e.g., a differential equation) is equipped with parameters. In practice, these parameters might be uncertain or noisy, and so an honest model should account for these uncertainties and provide a statistical description of the quantity of interest. Underlying this computational problem is a fundamental question - If two "similar" functions push-forward the same measure, are the new resulting measures close, and if so, in what sense? In this talk, I will first show how the probability density function (PDF) can be approximated, and present applications to nonlinear optics. We will then discuss the limitations of PDF approximation, and present an alternative Wasserstein-distance formulation of this problem, which through optimal-transport theory yields a simpler theory.

Bio: Amir Sagiv is a Chu Assistant Professor at Columbia University's department of Applied Physics and Applied Mathematics. Before that, Amir completed his M.Sc. and Ph.D. in Applied Mathematics at Tel Aviv University (2019), and his B.Sc. in Mathematics and Physics from the Hebrew University of Jerusalem (2009)