南方科技大学知识苑(SUSTech KC): Symbolic genetic algorithm for discovering open-form partial differential equations (SGA-PDE)

题名	Symbolic genetic algorithm for discovering open-form partial differential equations (SGA-PDE)
作者	Chen, Yuntian 1; Luo, Yingtao 2,3; Liu, Qiang 3; Xu, Hao 4,5; Zhang, Dongxiao6,7
通讯作者	Zhang, Dongxiao
发表日期	2022-06-01
DOI	10.1103/PhysRevResearch.4.023174
发表期刊	PHYSICAL REVIEW RESEARCH 影响因子和分区
EISSN	2643-1564
卷号	4 期号:2
摘要	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.
相关链接	[来源记录]
收录类别	ESCI ; EI
语种	英语
学校署名	通讯
资助项目	National Natural Science Foundation of China[62106116] ; Shenzhen Key Laboratory of Natural Gas Hydrates[ZDSYS20200421111201738]
WOS研究方向	Physics
WOS类目	Physics, Multidisciplinary
WOS记录号	WOS:000811625800004
出版者	AMER PHYSICAL SOC
EI入藏号	20222512246006
EI主题词	Binary trees ; Functions ; Iterative methods ; Korteweg-de Vries equation ; Nonlinear equations
EI分类号	Mathematics:921 ; Calculus:921.2 ; Numerical Methods:921.6
来源库	Web of Science
引用统计	被引频次[WOS]：34
成果类型	期刊论文
条目标识符	http://sustech.caswiz.com/handle/2SGJ60CL/343054
专题	南方科技大学
作者单位	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
通讯作者单位	南方科技大学
推荐引用方式 GB/T 7714	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).
APA	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).
MLA	Chen, Yuntian,et al."Symbolic genetic algorithm for discovering open-form partial differential equations (SGA-PDE)".PHYSICAL REVIEW RESEARCH 4.2(2022).