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

摘要 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.

doi： 10.34133/research.0147

作者： Hao Xu Junsheng Zeng Dongxiao Zhang

Author： Hao Xu Junsheng Zeng Dongxiao Zhang

作者单位： 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

刊名研究（英文） ISTICSCI

年，卷(期)： 2024, 2024(1)

机标分类号： TN957.71 TP391.9 G206

在线出版日期： 2024年4月15日

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