Data-driven solutions and parameter estimations of a family of higher-order KdV equations based on physics informed neural networks

• Published in: Scientific reports Vol. 14; no. 1; pp. 23874 - 27
• Main Authors: Chen, Jiajun, Shi, Jianping, He, Ao, Fang, Hui
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 12.10.2024; Nature Publishing Group; Nature Portfolio
• Subjects: 639/705; 639/705/1041; 639/705/1042; 639/705/117; 639/766; Data-driven solutions; Deep learning; Differential equations; Higher-order KdV equations; Humanities and Social Sciences; multidisciplinary; Neural networks; Parameter estimation; Parameter estimations; Partial differential equations; Physical informed neural network; Physics; Science; Science (multidisciplinary); Sine activation function; Sine activation function; Higher-order KdV equations; Data-driven solutions; Parameter estimations; Physical informed neural network
• ISSN: 2045-2322; 2045-2322
• DOI: 10.1038/s41598-024-74600-4

Physics informed neural network (PINN) demonstrates powerful capabilities in solving forward and inverse problems of nonlinear partial differential equations (NLPDEs) through combining data-driven and physical constraints. In this paper, two PINN methods that adopt tanh and sine as activation functions, respectively, are used to study data-driven solutions and parameter estimations of a family of high order KdV equations. Compared to the standard PINN with the tanh activation function, the PINN framework using the sine activation function can effectively learn the single soliton solution, double soliton solution, periodic traveling wave solution, and kink solution of the proposed equations with higher precision. The PINN framework using the sine activation function shows better performance in parameter estimation. In addition, the experiments show that the complexity of the equation influences the accuracy and efficiency of the PINN method. The outcomes of this study are poised to enhance the application of deep learning techniques in solving solutions and modeling of higher-order NLPDEs.