## Optimal Transport for Inverse Problems and the Implicit Regularization

#### 科研大讨论系列报告

### 报告题目(Title)：**Optimal Transport for Inverse Problems and the Implicit Regularization**

报告人(Speaker)：*杨雨楠 (Cornell University)*

地点(Place)：*后主楼1124*

时间(Time)：*2023 年12月22日（周五）上午8:30-9:30*

邀请人(Inviter)：*熊云丰*

### 报告摘要

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 metric space for numerical solution to PDEs.

### 主讲人简介

Yunan Yang is an applied mathematician working in inverse problems, optimization, and applied optimal transport. She is now a tenure-track Assistant Professor in the Department of Mathematics at Cornell University. Yunan Yang earned a Ph.D. degree in mathematics from the University of Texas at Austin in 2018, supervised by Prof. Bjorn Engquist. From September 2018 to August 2021, Yunan was a Courant Instructor at the Courant Institute of Mathematical Sciences, New York University, and then worked as an advanced fellow at the Institute for Theoretical Studies at ETH Zurich.