AM-GPINN algorithm and its application in a variable-coefficient resonant nonlinear Schrödinger equation

In this paper, we provide an effective deep learning model to predict the soliton solutions and their interactions of nonlinear partial differential equations (PDEs). Based on gradient information, we investigate the gradient-enhanced physics-informed neural networks (GPINN) method to improve the accuracy and training efficiency of PINN, which embeds the gradient of the residual into the neural network loss function. To further improve the …