Speaker: Yoonsang Lee, Dartmouth University

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 and 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 dynamic, such as rotation and outflow, that cannot be captured by the current state-of-the-art method, optimal transportation. This is joint work with Jihun Han at Dartmouth.

Bio: Yoonsang Lee is an assistant professor in the Department of Mathematics at Dartmouth College. His research focuses on applied mathematics and computational issues in prediction and uncertainty quantification of complex dynamical systems. He is interested in particular in computational methods to efficiently combine numerical prediction models with data, which are scalable for big data and high-dimensional systems.

This talk will be offered in a hybrid format. If you wish to participate remotely, please send an email to [email protected].