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

• Published in: Chaos, solitons and fractals solitons and fractals, 2022-11, Vol.164, p.112712, Article 112712
• Main Authors: Li, Jiaheng, Li, Biao
• Format: Article
• Language: English
• Subjects: Mixed training; NLS equation; Physics-informed neural networks; Prior information; Rogue waves
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2022.112712

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. •Hybrid training idea. After mixed training the sample points of initial value and boundary of the nonlinear partial differential equation (The other models are trained separately), the robustness is greatly improved.•Adaptive search algorithm. Through the adaptive search algorithm, the points with large gradient within the prediction range of the solution are searched as prior information and added into the model, and the prediction ability of the model is significantly improved.•The relative error is small and stable. Compared with the traditional PINNs model, the model proposed in this paper is very small and stable in training error, and has a significant improvement in prediction accuracy.•Stronger predictive performance. When the range of the predicted solution becomes larger or the solution has a local sharp region, the prediction performance is still very good.