A-WPINN algorithm for the data-driven vector-soliton solutions and parameter discovery of general coupled nonlinear equations

• Published in: Physica. D 2023-01, Vol.443, p.133562, Article 133562
• Main Authors: Qin, Shu-Mei, Li, Min, Xu, Tao, Dong, Shao-Qun
• Format: Article
• Language: English
• Subjects: A-WPINN; Deep learning; N-coupled nonlinear equation; Parameters discovery; Vector N-soliton solutions
• ISSN: 0167-2789; 1872-8022
• DOI: 10.1016/j.physd.2022.133562

This work aims to provide an effective deep learning framework to predict the vector-soliton solutions of the coupled nonlinear equations and their collisions. The method we propose here is a weighted physics-informed neural network (WPINN) combining with the adaptive residual points distribution (A-WPINN) algorithm. Different from the traditional PINN algorithm which takes points randomly, the A-WPINN algorithm uses an adaptive point-fetching approach to improve the training efficiency for the solutions with steep gradients. Furthermore, the A-WPINN algorithm weights the training samples to achieve the goal of accelerating the learning progress. We implement series of experimental comparisons between the A-WPINN and traditional PINN algorithms with a generalized coupled nonlinear Schrödinger (GCNLS) equation as an example. The results indicate that the A-WPINN algorithm has faster convergence rate and better approximation ability. Finally, the A-WPINN method is applied to the data-driven parameters discovery of the equation, which shows the dispersion and nonlinear coefficients can be well approximated. •A weighted PINN with the adaptive residual points distribution algorithm is proposed.•The accuracy of predicted vector solutions gets improved by one order of magnitude.•The new method has good performance in the parameter discovery of the GCNLS equations.•Such method can be applied to learning vector nonlinear waves of other coupled systems.