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Directors:
Randolph E. Bank
Philip E. Gill
Michael Holst

Administrative Contact:
Jennifer Trefftzs

Office: AP&M 7409
Phone: (858)534-9056
Fax: (858)534-5273
E-mail: jtrefftzs@ucsd.edu
Local and optimal transport perspectives on uncertainty propagation

Amir Sagiv
Columbia University

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 provide a statistical description of the quantity of interest. Underlying this computational question is a fundamental one - If two "similar" functions push-forward the same measure, are the new resulting measures close, and if so, in what sense? I will first show how the probability density function (PDF) can be approximated, using spectral and local methods, 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 yields a much simpler theory.

Tuesday, March 30, 2021
11:00AM Zoom ID 939 3177 8552