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

• DOI: 10.34133/research.0147
• Publication Date: 2023-04-29T03:47:36Z
• Authors: Hao Xu; Junsheng Zeng; Dongxiao Zhang
• Keywords: Robustness; Proposition

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