Data-driven rogue waves and parameters discovery in nearly integrable [formula omitted]-symmetric Gross–Pitaevskii equations via PINNs deep learning

Abstract

In this paper, we explore the forward and inverse problems for the generalized Gross–Pitaevskii (GP) equation with complex PT-symmetric potentials via the deep physics-informed neural networks (PINNs). The data-driven rogue waves (RWs) are mainly studied in the forward problem, where the comparisons between the data-driven RWs and numerical ones via the spectral method are used to present the PINNs solution accuracies. Besides, we also focus on the influences of several critical factors (e.g., the depths of neural networks, numbers of training points) on the performance of the PINNs algorithm. Finally, the inverse problem is also investigated such that the system parameters can be identified from the training data. The results obtained in this paper can be useful to further understand the neural networks on rogue wave structures in the nearly integrable PT-symmetric nonlinear wave systems.