Data-driven SFB solutions and parameters discovery for nonlinear Schrödinger equation via time domain decomposition physics-informed neural networks

In this paper, we integrate domain decomposition techniques into the classical physics-informed neural networks (PINNs) by introducing interface training points, and propose a time domain decomposition PINNs (TDD-PINNs) framework. This model is applied to investigate the dynamic behaviour of solitons on finite background (SFB) solutions and parameter discovery in the nonlinear Schrödinger equation (NLSE). The TDD-PINNs is employed to study various SFB solutions, including the Akhmediev breather, Peregrine soliton, Kuznetsov-Ma soliton, as well as second- and third-order rogue waves. Experimental results demonstrate that, compared to classical PINNs, the proposed TDD-PINNs significantly reduce training time and improve prediction accuracy by one to two orders of magnitude. For inverse problems, the TDD-PINNs algorithm can accurately identify unknown parameters in the NLSE, both under noisy and noise-free conditions, addressing the complete failure of classical PINNs in parameter identification for NLSE and demonstrating strong robustness.