Automated partial differential equation identification

Ruixian Liu; Michael J Bianco; Peter Gerstoft

doi:10.1121/10.0006444

Automated partial differential equation identification

J Acoust Soc Am. 2021 Oct;150(4):2364. doi: 10.1121/10.0006444.

Authors

Ruixian Liu¹, Michael J Bianco², Peter Gerstoft²

Affiliations

¹ Department of Electrical and Computer Engineering, University of California, San Diego, California 92161, USA.
² Scripps Institution of Oceanography, University of California San Diego, La Jolla, California 92037, USA.

PMID: 34717467
DOI: 10.1121/10.0006444

Abstract

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.