Mini-symposium (MS) 

MS11:  Recent Progress of Classical and Deep Learning Methods in Inverse Problems and Imaging

Organizers: Xiaojing Ye, Georgia State University

                     Yang Yang, Michigan State University

Abstract: Inverse problems seek to infer causal factors from observations. They arise naturally in a wide range of scientific fields, especially in imaging sciences and technologies. Classical approaches towards inverse problems explore the relation between causal factors and observations using tools from various mathematical branches including partial differential equations, functional analysis, optimization, numerical analysis, and probability theory. On the other hand, recent decades have witnessed an emerging trend of using deep learning (DL) methods to solve inverse problems. Compared to classical approaches, DL methods shed new light on solving several fundamental challenges in inverse problems such as the curse of dimensionality and ill-posedness. The aim of this mini-symposium is to bring together applied mathematicians in the area of inverse problems to discuss recent progress of classical and DL methods. The mini-symposium is expected to promote the development of novel ideas and new research collaborations through knowledge dissemination and discussion.

Saturday, September 18, 10:00 AM – 12:00 PM: Part I of II

Room: Libry 4127

10:00 – 10:30 Chunmei Wang, University of Florida, Structure probing neural network deflation

10:30 – 11:00 Yunan Yang, New York University, Optimal transport for parameter identification of chaotic dynamics via invariant measures

11:00 – 11:30 Haizhao Yang, Purdue University, Deep learning theory for solving PDEs: approximation, optimization, and generalization

11:30 – 12:00 Alexandra Smirnova, Georgia State University, Model predictions in epidemiology by using stable parameter estimation and real data

Sunday, September 19, 10:30 AM – 12:30 PM: Part II of II

Room: Libry 3127

10:30 – 11:00 Wuchen Li, University of South Carolina, Neural primal dual methods for mean field games

11:00 – 11:30 Yimin Zhong, Duke University, Quantitative PAT with simplified $P_N$ approximation

11:30 – 12:00 Christina Frederick, New Jersey Institute of Technology, Machine learning for inverse problems in sonar imaging

12:00 – 12:30 Rongjie Lai, Rensselaer Polytechnic Institute, Geometry inspired DNNs on manifold-structured data