Adaptive decoupling parallel physics-informed neural networks for integrable coupled NLS equations

Abstract An adaptive decoupling parallel physics-informed neural network (AD-PPINN) is proposed for data-driven parameter discovery and solution prediction of integrable coupled nonlinear Schrödinger (NLS) equations. By analyzing the influence of nonlinear parameters on the prediction accuracy of PINNs for the single NLS equation and considering the inherent decoupling behavior of integrable coupled NLS equations, adaptive transformation parameters are incorporated as learnable parameters of the neural network to improve prediction accuracy. Additionally, to enhance the guidance of the physical model, an additional term is incorporated into the loss function for the parameter discovery, derived from the corresponding relationship between parameters under two new physical constraints after decoupling. Comparative experiments and ablation studies are performed to systematically assess the performance of AD-PPINN and to quantify the contribution of different components. In addition, sensitivity analyses are carried out to examine the robustness of AD-PPINN with respect to the initializations of transformation parameters, the choice of regularization coefficients, the size of dataset, and the presence of noise. The experimental results demonstrate that AD-PPINN is effective and robustness in addressing data-driven problems of integrable coupled NLS equations that satisfy the decoupling condition.