Nonlinear Wave Dynamics Research And Data-Driven Model Discovery Via Deep Learning

Physics-informed neural network（PINN）can be used to predict various solutions of nonlinear partial differential equations in diverse physical fields.In order to explore data-driven solutions to partial differential equations and parameter discovery based on data-driven,in this paper,PINN model is introduced firstly,while discussing the current state of domestic and international research on the Sasa-Satsuma equation.The PINN algorithm is then used to simulate the evolutionary form of various types of nonlinear waves,while the study of the inverse problem of partial differential equations when the equation coefficients are unknown is considered.This paper mainly includes three aspects:Firstly,the PINN is used to predict（single-）double-hump soliton,multi-hump breather,anti-dark soliton,Mexican-hat soliton,twisted rogue-wave pairs and rational W-shaped soliton of the Sasa-Satsuma equation in optical fibers and deep water wave.The L₂ relative error of the prediction results can achieve high accuracy even with only less training data and training time while the results show that the prediction error will increase with the increase of prediction time.Secondly,the inverse problem of the equation,i.e.the parametric discovery of the equation coefficients,is investigated using the PINN algorithm to predict the unknown coefficients of the Sasa-Satsuma equation and solve it.The effectiveness of the PINN method is also verified by adding different levels of noise to the experimental data.Finally,the PINN method is compared with the traditional numerical methods in terms of prediction results and data volume,and their advantages and disadvantages are analysed and discussed.The results show that the PINN method requires less data under the condition that the same accuracy is achieved in the prediction results.