DLGA-PDE: Discovery of PDEs with incomplete candidate library via combination of deep learning and genetic algorithm

Xu，Hao1; Chang，Haibin1; Zhang，Dongxiao2,3

2020-10-01

10.1016/j.jcp.2020.109584

JOURNAL OF COMPUTATIONAL PHYSICS   影响因子和分区

0021-9991

1090-2716

Data-driven methods have recently been developed to discover underlying partial differential equations (PDEs) of physical problems. However, for these methods, a complete candidate library of potential terms in a PDE are usually required. To overcome this limitation, we propose a novel framework combining deep learning and genetic algorithm, called DLGA-PDE, for discovering PDEs. In the proposed framework, a deep neural network that is trained with available data of a physical problem is utilized to generate meta-data and calculate derivatives, and the genetic algorithm is then employed to discover the underlying PDE. Owing to the merits of the genetic algorithm, such as mutation and crossover, DLGA-PDE can work with an incomplete candidate library. The proposed DLGA-PDE is tested for discovery of the Korteweg–de Vries (KdV) equation, the Burgers equation, the wave equation, and the Chaffee-Infante equation, respectively, for proof-of-concept. Satisfactory results are obtained without the need for a complete candidate library, even in the presence of noisy and limited data.

Deep neural network Genetic algorithm Incomplete candidate library Machine learning PDE discovery

SCI ; EI

英语

其他

National Natural Science Foundation of China[51520105005][U1663208] ; National Science and Technology Major Project of China[2017ZX05009-005][2017ZX05049-003]

Computer Science ; Physics

Computer Science, Interdisciplinary Applications ; Physics, Mathematical

WOS:000561583600006

ACADEMIC PRESS INC ELSEVIER SCIENCE

20203008976417

Genetic algorithms ; Learning algorithms ; Partial differential equations

Ergonomics and Human Factors Engineering:461.4 ; Machine Learning:723.4.2 ; Calculus:921.2

PHYSICS

2-s2.0-85088365166

Scopus

1.BIC-ESAT,ERE,SKLTCS,College of Engineering,Peking University,Beijing,100871,China
2.School of Environmental Science and Engineering,Southern University of Science and Technology,Shenzhen,518055,China
3.Intelligent Energy Lab,Peng Cheng Laboratory,Shenzhen,518000,China

Xu，Hao,Chang，Haibin,Zhang，Dongxiao. DLGA-PDE: Discovery of PDEs with incomplete candidate library via combination of deep learning and genetic algorithm[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2020,418.

Xu，Hao,Chang，Haibin,&Zhang，Dongxiao.(2020).DLGA-PDE: Discovery of PDEs with incomplete candidate library via combination of deep learning and genetic algorithm.JOURNAL OF COMPUTATIONAL PHYSICS,418.

Xu，Hao,et al."DLGA-PDE: Discovery of PDEs with incomplete candidate library via combination of deep learning and genetic algorithm".JOURNAL OF COMPUTATIONAL PHYSICS 418(2020).