Thursday, October 3rd 2024
11:00 AM - 11:50 AM
Stratton Hall 207
Title: Solving PDEs and learning dynamical systems using neural networks
Abstract: : This talk has two parts. In the first part, I will discuss the derivative-free loss method for solving PDEs, its analysis, and applications to multiscale problems and perforated domains. The second part discusses a project related to learning in between images. The new approach incorporates a PDE model in the latent space to assist the learning process. This approach shows robust results in capturing challenging dynamics, such as rotation and outflow, that cannot be captured by the current state-of-the-art method, the optimal transportation. This is joint work with Jihun Han at Dartmouth.
