Prediction of multipole vector solitons and model parameters for coupled saturable nonlinear Schrödinger equations

We construct the extended physics-informed neural network with dual subnets to study the coupled saturable nonlinear Schrödinger equation, and predict the dipole-dipole, tripole-dipole and dipole-tripole vector soliton solutions. From the comparison between prediction and numerical solutions, evolutionary process prediction and loss function, the extended physics-informed neural network can be used to solve the coupled saturable nonlinear Schrödinger equation, and continuously optimize the prediction of model parameters by improving learning rate and loss function. The errors of dipole-dipole, tripole-dipole and dipole-tripole vector soliton solutions increase along the transmission distance, and they are mainly concentrated in the middle part of soliton structures. Moreover, model parameters are predicted through three different types of input data, and predicted results are compared. These results have certain reference value for predicting the transmission process of optical solitons using the machine learning.