The data-driven rogue waves of the Hirota equation by using Mix-training PINNs approach

• Published in: Physica. D 2024-09, Vol.465, p.134202, Article 134202
• Main Authors: Sun, Shi-fei, Tian, Shi-fang, Li, Biao
• Format: Article
• Language: English
• Subjects: Hirota equation; Mixed training; Physics-informed neural networks; Prior information; Rogue waves
• ISSN: 0167-2789; 1872-8022
• DOI: 10.1016/j.physd.2024.134202

Recently, solving differential equations by deep neural networks has attracted lots of attention, however, when the solution of differential equations has localized areas such as the rogue waves, the classical physics-informed neural networks (PINNs) cannot guarantee its prediction accuracy. In this paper, we propose two neural networks methods: mix-training physics-informed neural networks (MTPINNs) and prior information mix-training physics-informed neural networks (PMTPINNs), two deep learning models with more approximation ability based on PINNs. A series of numerical experiments show that the learning efficiency and absolute error accuracy of our proposed model can be improved significantly. The PMTPINNs model can so as to make up for the shortcomings of PINNs in this aspect. Furthermore, by testing the robustness of these two methods, for two kinds of rogue waves of the Hirota equation, it is surprising that these models also have good performance and thereby may provide more possibilities for solving mathematical physics problems better. •Two neural networks methods have been proposed to study the high-order rogue waves of the Hirota equation.•The MTPINNs and the PMTPINNs yield considerable improvement in accuracy and have good robustness.•We propose the adjusted PMTPINNs+, which further improves the learning and prediction ability of PMTPINNs.