Data-driven prediction of soliton solutions of the higher-order NLSE via the strongly-constrained PINN method

Abstract

We propose a strongly-constrained physics-informed neural network method with the derivative information to more suitably predict soliton dynamics of the nonlinear partial differential equation. We integrate more constrained physical information into the neural network, namely we add the derivative information of solutions for the nonlinear partial differential equation to the neural network structure, and introduce adaptive weight and flexible learning rate, to accelerate the convergence of the loss function of the network. As an example, we use this new method to predict a variety of soliton solutions of higher-order nonlinear Schrödinger equation. Moreover, we introduce the derivative of soliton solution to further reflect the stability of the data set. Results show that this new method can achieve the prediction in a wider solution area than the traditional method. Compared with results in previous literatures, the accuracy of the strongly-constrained physics-informed neural network method in predicting soliton dynamics is improved by 2-12 times. Therefore, this neural network is a forward-looking technology for scientific computing and automatic modeling.