Prediction of symmetric and asymmetric solitons and model parameters for nonlinear Schrödinger equations with competing nonlinearities

he modified physics-informed neural network method with the learning rate decay is used to study two types of non-integrable nonlinear Schrödinger equations with competing nonlinearities. Symmetric and asymmetric solitons of nonlinear Schrödinger equations with competing quadratic-cubic and cubic-quintic nonlinearities are respectively predicted. The predicted results are presented from multiple aspects such as evolution process, error and loss function, which shows that the modified physical information neural network can effectively predict dynamics of these symmetric and asymmetric solitons in two cases of competing nonlinearities. From the error graphs of numerical and predictive solutions, the error gradually increases and mainly concentrates on the peak parts as the transmission distance increases. By setting appropriate loss function and improving the learning rate, iteration times and other aspects, model parameters are predicted successfully, and the influence of different number of iterations, neurons and hidden layers on the prediction error is compared. These findings have the certain reference value for using machine learning to predict the dynamics of optical solitons for non-integrable models.