Discovery of Partial Differential Equations from Highly Noisy and Sparse Data with Physics-Informed Information Criterion
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.
Key Laboratory of Renewable Energy and Natural Gas Hydrate, Chinese Academy of Sciences[ZDSYS20200421111201738];
Cited Times [WOS]:0
|Document Type||Journal Article|
|Department||National Center for Applied Mathematics, SUSTech Shenzhen|
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
|Corresponding Author Affilication||National Center for Applied Mathematics, SUSTech Shenzhen|
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).
|Files in This Item:||There are no files associated with this item.|
|Recommend this item|
|Export to Endnote|
|Export to Excel|
|Export to Csv|
|Similar articles in Google Scholar|
|Similar articles in Baidu Scholar|
|Similar articles in Bing Scholar|
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.