Special Colloquium- Shixu Meng, Virginia Tech

Exploring Low-Rank Structures in Inverse Scattering and Matrix Differential Equations

When

3:30 – 4:30 p.m., Feb. 10, 2025

Where

Title: 
Exploring Low-Rank Structures in Inverse Scattering and Matrix Differential Equations
 
Abstract: 
The inverse scattering problem plays an important role in a wide range of physical and engineering applications where hidden or internal features need to be imaged. It is a very challenging problem because inverse scattering is intrinsically nonlinear and ill-posed, and the measurement data are inevitably corrupted by noise. To address this challenge and bridge the gap between data science and inverse scattering, I will demonstrate a low-rank structure tailored for inverse scattering and discuss a regularized numerical method with an explicit stability estimate. The idea of low-rank structures is also useful for solving forward problems. In the second part of the talk, I will show preconditioned low-rank Krylov methods for implicit discretizations of matrix differential equations. Finally, I will conclude with a discussion on my future research plans.
 
Refreshments will be served in the Math Commons Room at 3:00pm