Data-driven fusion and fission solutions in the Hirota–Satsuma–Ito equation via the physics-informed neural networks method

Abstract

Fusion and fission are two important phenomena that have been experimentally observed in many real physical models. In this paper, we investigate the two phenomena in the (2+1)-dimensional Hirota–Satsuma–Ito equation via the physics-informed neural networks (PINN) method. By choosing suitable physically constrained initial boundary conditions, the data-driven fusion and fission solutions are obtained for the first time. Dynamical behaviors and error analysis of these solutions are investigated via illustratively numerical figures, which show that good results are achieved. It is pointed out that the PINN method adopted here can be effectively used to construct the data-driven fusion and fission solutions for other nonlinear integrable equations. Based on the powerful predictive capability of the PINN method and wide applications of fusion and fission in many physical areas, it is hoped that the data-driven solutions obtained here will be helpful for experts to predict or explain related physical phenomena.