Physics-informed Neural Network method for predicting soliton dynamics supported by complex PT-symmetric potentials

Abstract

Abstract We examine the deep learning technique referred to as the physics-informed neural network method for approximating non-linear Schrödinger equation under considered parity time symmetric potentials and obtaining multifarious soliton solutions. For the first time, neural networks founded principally physical information are adopted to figure out the solution the examined non-linear partial differential equation and 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 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. Besides, we also 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 non-linear Schrödinger equation under consideration and predict the dynamics of soliton solution.