Automated partial differential equation identification
Ruixian Liu1, Michael J Bianco2, Peter Gerstoft2
1Department of Electrical and Computer Engineering, University of California, San Diego, California 92161, USA.
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.
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