Symbolic genetic algorithm for discovering open-form partial differential equations (SGA-PDE)

Chen, Yuntian1; Luo, Yingtao2,3; Liu, Qiang3; Xu, Hao4,5; Zhang, Dongxiao6,7

2022-06-01

10.1103/PhysRevResearch.4.023174

PHYSICAL REVIEW RESEARCH   Impact Factor & Quartile

2643-1564

Partial differential equations (PDEs) are concise and understandable representations of domain knowledge, which are essential for deepening our understanding of physical processes and predicting future responses. However, the PDEs of many real-world problems are uncertain, which calls for PDE discovery. We propose the symbolic genetic algorithm to discover open-form PDEs (SGA-PDE) directly from data without prior knowledge about the equation structure. SGA-PDE focuses on the representation and optimization of PDEs. Firstly, SGA-PDE uses symbolic mathematics to realize the flexible representation of any given PDE, transforms a PDE into a forest, and converts each function term into a binary tree. Secondly, SGA-PDE adopts a specially designed genetic algorithm to efficiently optimize the binary trees by iteratively updating the tree topology and node attributes. The SGA-PDE is gradient free, which is a desirable characteristic in PDE discovery since it is difficult to obtain the gradient between the PDE loss and the PDE structure. In the experiment, SGA-PDE not only successfully discovered the nonlinear Burgers' equation, the Korteweg-de Vries equation, and the Chafee-Infante equation but also handled PDEs with fractional structure and compound functions that cannot be solved by conventional PDE discovery methods.

ESCI ; EI

English

Corresponding

National Natural Science Foundation of China[62106116] ; Shenzhen Key Laboratory of Natural Gas Hydrates[ZDSYS20200421111201738]

Physics

Physics, Multidisciplinary

WOS:000811625800004

AMER PHYSICAL SOC

20222512246006

Binary trees ; Functions ; Iterative methods ; Korteweg-de Vries equation ; Nonlinear equations

Mathematics:921 ; Calculus:921.2 ; Numerical Methods:921.6

Web of Science

1.Yongriver Inst Technol, Eastern Inst Adv Study, Ningbo 315201, Zhejiang, Peoples R China
2.Univ Washington, Dept Comp Sci, Seattle, WA 98195 USA
3.RealAI, Beijing 100085, Peoples R China
4.Peking Univ, Beijing Innovat Ctr Engn Sci & Adv Technol BIC ES, Energy & Resources Engn ERE, Coll Engn, Beijing 100871, Peoples R China
5.Peking Univ, State Key Lab Turbulence & Complex Syst SKLTCS, Coll Engn, Beijing 100871, Peoples R China
6.Southern Univ Sci & Technol, Natl Ctr Appl Math Shenzhen NCAMS, Shenzhen 518055, Guangdong, Peoples R China
7.Peng Cheng Lab, Dept Math & Theories, Shenzhen 518000, Guangdong, Peoples R China

Chen, Yuntian,Luo, Yingtao,Liu, Qiang,et al. Symbolic genetic algorithm for discovering open-form partial differential equations (SGA-PDE)[J]. PHYSICAL REVIEW RESEARCH,2022,4(2).

Chen, Yuntian,Luo, Yingtao,Liu, Qiang,Xu, Hao,&Zhang, Dongxiao.(2022).Symbolic genetic algorithm for discovering open-form partial differential equations (SGA-PDE).PHYSICAL REVIEW RESEARCH,4(2).

Chen, Yuntian,et al."Symbolic genetic algorithm for discovering open-form partial differential equations (SGA-PDE)".PHYSICAL REVIEW RESEARCH 4.2(2022).