Physics-Informed Neural Network Method for Predicting Soliton Dynamics Supported by Complex Parity-Time Symmetric Potentials

Abstract

We examine the deep learning technique referred to as the physics-informed neural network method for approximating the nonlinear Schrödinger equation under considered parity-time symmetric potentials and for obtaining multifarious soliton solutions. Neural networks to found principally physical information are adopted to figure out the solution to the examined nonlinear partial differential equation and to generate six different types of soliton solutions, which are basic, dipole, tripole, quadruple, pentapole, and sextupole solitons we consider. We make comparisons between the predicted and actual soliton solutions to see whether deep learning is capable of seeking the solution to the partial differential equation described before. We may assess whether physics-informed neural network is capable of effectively providing approximate soliton solutions through the evaluation of squared error between the predicted and numerical results. Moreover, we scrutinize how different activation mechanisms and network architectures impact the capability of selected deep learning technique works. Through the findings we can prove that the neural networks model we established can be utilized to accurately and effectively approximate the nonlinear Schrödinger equation under consideration and to predict the dynamics of soliton solution.