PINN-Based Multi-Scene Modeling Of Nonlinear Dynamics

In this paper,a physics-informed neural network(PINN)that combines deep learning and physics is investigated to solve the nonlinear Schrodinger equation that describes the nonlinear dynamics in optical fibers.This paper mainly considers three different nonlinear Schr?dinger equations with different PT-symmetric potentials,namely Gaussian potential,periodic potential,and Rosen-Morse potential,and uses PINN for approximate solutions.The study compares the predicted results with actual results and analyzed the ability of deep learning to solve the considered partial differential equations.The ability of PINN to approximate soliton solutions is examined by calculating the square error between the actual values and the predicted values.Additionally,the influence of different activation functions(ReLU,sigmoid,tanh,and sech)on the performance of the considered deep learning approach is explored.In addition to these topics,this paper demonstrates the network structure and how it affects the performance of physics-inspired neural networks.The results show that the constructed deep learning model can accurately approximate the soliton solutions of the considered equation.