Speaker: Yimin Zhong, Auburn University

Title: How much can one learn a PDE from its solution?

Abstract: In this work we study a few basic questions for PDE learning from observed solution data. Using various types of PDEs, we show 1) how the approximate dimension (richness) of the data space spanned by all snapshots along a solution trajectory depends on the differential operator and initial data, and 2) identifiability of a differential operator from solution data on  local patches. Then we propose a consistent and sparse local regression method (CaSLR) for general PDE identification. Our method is data driven and requires minimal amount of local measurements in space and time from a single solution trajectory by enforcing global consistency and sparsity.

Bio: Yimin Zhong is an Assistant Professor of Mathematics and Statistics at Auburn University. He received his Ph.D. at the University of Texas at Austin in 2017, where he was advised by Professor Kui Ren. His research interests mainly focus on applied mathematics and scientific computing. In particular, he is currently interested in data-driven modeling, the intrinsic complexity of datasets, inverse problems,  fast algorithms, multiphysics modeling, etc.

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