Data-driven solutions of coherently coupled nonlinear Schrödinger model via a customized parallel physics-informed neural network

Abstract A customized parallel physics-informed neural networks (cPPINN) is proposed to predict data-driven solutions of coherently coupled nonlinear Schrödinger equation. Different from the parallel physics-informed neural networks presented in previous literature, the parallel architecture in this paper is designed based on the inherent property of the physical model. It takes the relationship among nonlinearity parameters as prior knowledge to reduces the complexity of the physical constraints through a linear transformation. Moreover, a modified cPPINN is proposed by embedding the gradient information of partial differential equation residuals into the cPPINN to further improve the prediction accuracy. To verify the performance of the algorithm, we predict the data-driven solutions in nonlocal and local coupled systems. Computational results reveal that, compared to conventional physics-informed neural networks, the cPPINN and modified cPPINN markedly enhance the prediction accuracy of solutions. The proposed approaches can be directly extended to higher dimension systems as the transformation and its condition are not affected by the high-dimensional contexts.