Name: Yunan Yang
Date: Thursday, January 28, 2021 at 11:00 am
Title: Optimal Transport for Inverse Problems and the Implicit Regularization
Abstract: Optimal transport has been one interesting topic of mathematical analysis since Monge (1781). The problem's close connections with differential geometry and kinetic descriptions were discovered within the past century, and the seminal work of Kantorovich (1942) showed its power to solve real-world problems. Recently, we proposed the quadratic Wasserstein distance from optimal transport theory for inverse problems, tackling the classical least-squares method's longstanding difficulties such as nonconvexity and noise sensitivity. The work was soon adopted in the oil industry. As we advance, we discover that the advantage of changing the data misfit is more general in a broader class of data-fitting problems by examining the preconditioning and "implicit" regularization effects of different mathematical metrics as the objective function in optimization, as the likelihood function in Bayesian inference, and as the measure of residual in numerical solution to PDEs.
Bio: Yunan Yang joined NYU in 2018 as a Courant Instructor, after earning her Ph.D. in Mathematics under the supervision of Dr. Bjorn Engquist from the University of Texas at Austin. Her dissertation was interdisciplinary research between numerical analysis and geophysics, mainly focusing on analyzing and applying optimal transport and inverse problems. In the year 2019, Yunan was honored as one of thirty-two "Rising Stars in Computational and Data Sciences" from a strong pool of nominations by Oden Institute at the University of Texas at Austin. She was a selected participant of the 7th Heidelberg Laureate Forum (HLF) in Germany. Yunan received First Place in the 19th IMA Leslie Fox Prize in numerical analysts.