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

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

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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.

Hao Xu、Junsheng Zeng、Dongxiao Zhang

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BIC-ESAT,ERE,and SKLTCS,College of Engineering,Peking University,Beijing 100871,P.R.China

Institute of Applied Physics and Computational Mathematics,Beijing 100088,P.R.China

Eastern Institute for Advanced Study,Eastern Institute of Technology,Ningbo 315200,Zhejiang,P.R.China

National Center for Applied Mathematics Shenzhen(NCAMS),Southern University of Science and Technology,Shenzhen 518055,Guangdong,P.R.China

Department of Mathematics and Theories,Peng Cheng Laboratory,Shenzhen 518000,Guangdong,P.R.China

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National Center for Applied Mathematics Shenzhen(NCAMS)Shenzhen Key Laboratory of Natural Gas HydratesSUSTech-Qingdao New Energy Technology Research Institute

ZDSYS20200421111201738

2024

10.34133/research.0147

研究(英文)

研究(英文)

CSTPCD
ISSN：
年,卷(期)：2024.2024(1)
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