Discovery of Partial Differential Equations from Highly Noisy and Sparse Data with Physics-Informed Information Criterion.

ABSTRACT: Data-driven discovery of partial differential equations (PDEs) has recently made tremendous progress, and many canonical PDEs have been discovered successfully for proof of concept. However, determining the most proper PDE without prior references remains challenging in terms of practical applications. In this work, a physics-informed information criterion (PIC) is proposed to measure the parsimony and precision of the discovered PDE synthetically. The proposed PIC achieves satisfactory robustness to highly noisy and sparse data on 7 canonical PDEs from different physical scenes, which confirms its ability to handle difficult situations. The PIC is also employed to discover unrevealed macroscale governing equations from microscopic simulation data in an actual physical scene. The results s

SUBMITTER: Xu H 

PROVIDER: S-EPMC10198462 | biostudies-literature | 2023

REPOSITORIES: biostudies-literature