Automated partial differential equation identification

Inspired by recent developments in data-driven methods for partial differential equation (PDE) estimation, we use sparse modeling techniques to automatically estimate PDEs from data. A dictionary consisting of hypothetical PDE terms is constructed using numerical differentiation. Given data, PDE terms are selected assuming a parsimonious representation, which is enforced using a sparsity constraint. Unlike previous PDE identification schemes, we make no assumptions about which PDE terms are responsible for a given field. The approach is demonstrated on synthetic and real video data, with physical phenomena governed by wave, Burgers, and Helmholtz equations. Codes are available at https://github.com/NoiseLab-RLiu/Automate-PDE-identification.