1. Automated partial differential equation identification
- Author
-
Ruixian Liu, Peter Gerstoft, and Michael J. Bianco
- Subjects
Constraint (information theory) ,Identification (information) ,Partial differential equation ,Acoustics and Ultrasonics ,Arts and Humanities (miscellaneous) ,Helmholtz equation ,Computer science ,Physical phenomena ,Numerical differentiation ,Applied mathematics ,Field (mathematics) ,Representation (mathematics) ,Mathematics::Numerical Analysis - 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.
- Published
- 2021