Mathematical Analysis and Numerical Methods for Inverse Scattering Problems

Explore the intricacies of inverse scattering problems in this 46-minute lecture by Gang Bao for the International Mathematical Union. Delve into mathematical analysis and numerical methods, covering topics such as the Radon Transform, Calderón Problem, and stability analysis. Gain insights into inverse medium problems, numerical results, and the application of deep learning algorithms for inverse problems. Learn about the challenges and recent progress in the field of inverse scattering, equipping yourself with advanced knowledge in this complex area of mathematical physics.

Intro
Outline
Introduction: Scattering and Inverse Scattering
Application: Radon Transform
Calderón Problem: Progress and Challenges
Challenges for Inverse Scattering
Inverse Scattering Problems
Inverse Scattering Algorithms
Inverse Medium Problems: Progress
Numerical Results
Stability Analysis
Stability for ISP
Deep Learning Based Algorithms for IPs