Title: Learn PDE from its solution 

 

 

Abstract: In this talk, I will discuss our motivation and address a few basic questions about learning the PDE from observed solution data, as well as how I considered these questions in the project. The talk will take a few types of PDEs as examples to 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 I will discuss the consistent and sparse local regression method (CaSLR) for general PDE identification. The process is data-driven and requires minimal local measurements in space and time from a single solution trajectory, enforcing global consistency and sparsity.