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

Xu，Hao1; Zeng，Junsheng2; Zhang，Dongxiao3,4,5

2023

10.34133/research.0147

Research   Impact Factor & Quartile

2096-5168

2639-5274

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 show that the discovered macroscale PDE is precise and parsimonious and satisfies underlying symmetries, which facilitates understanding and simulation of the physical process. The proposition of the PIC enables practical applications of PDE discovery in discovering unrevealed governing equations in broader physical scenes.

English

Corresponding

Key Laboratory of Renewable Energy and Natural Gas Hydrate, Chinese Academy of Sciences[ZDSYS20200421111201738];

2-s2.0-85163378884

Scopus

1.BIC-ESAT,ERE,and SKLTCS,College of Engineering,Peking University,Beijing,100871,China
2.Institute of Applied Physics and Computational Mathematics,Beijing,100088,China
3.Eastern Institute for Advanced Study,Eastern Institute of Technology,Ningbo,Zhejiang,315200,China
4.National Center for Applied Mathematics Shenzhen (NCAMS),Southern University of Science and Technology,Shenzhen,Guangdong,518055,China
5.Department of Mathematics and Theories,Peng Cheng Laboratory,Shenzhen,Guangdong,518000,China

Xu，Hao,Zeng，Junsheng,Zhang，Dongxiao. Discovery of Partial Differential Equations from Highly Noisy and Sparse Data with Physics-Informed Information Criterion[J]. Research,2023,6.

Xu，Hao,Zeng，Junsheng,&Zhang，Dongxiao.(2023).Discovery of Partial Differential Equations from Highly Noisy and Sparse Data with Physics-Informed Information Criterion.Research,6.

Xu，Hao,et al."Discovery of Partial Differential Equations from Highly Noisy and Sparse Data with Physics-Informed Information Criterion".Research 6(2023).