Mix-training physics-informed neural networks for the rogue waves of nonlinear Schrödinger equation

Abstract

In this paper, we propose mix-training physics-informed neural networks (PINNs). This is a deep learning model with more approximation ability based on PINNs, combined with mixed training and prior information. We demonstrate the advantages of this model by exploring rogue waves with rich dynamic behavior in the nonlinear Schrödinger (NLS) equation. Compared with the original PINNs, numerical results show that this model can not only quickly recover the dynamical behavior of the rogue waves of NLS equation, but also improve its approximation ability and absolute error accuracy significantly, and the prediction accuracy has been improved by two to three orders of magnitude. In particular, when the space–time domain of the solution expands, or the solution has a local sharp region, the proposed model still has high prediction accuracy.