Data-Driven Rogue Waves in Nonlocal PT-Symmetric Schr?dinger Equation via Mix-Training PINN

作     者：SUN Jiawei LI Biao 

作者机构：School of Mathematics and Statistics Ningbo University 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报(英文版))

年 卷 期：2024年

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 081104[工学-模式识别与智能系统] 08[工学] 0835[工学-软件工程] 070102[理学-计算数学] 0811[工学-控制科学与工程] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：supported by the National Natural Science Foundation of China under Grant Nos. 12175111,12275144, and 12235007 K.C. Wong Magna Fund in Ningbo University 

摘      要：In this paper, by modifying loss function MSE(adding the mean square error of the complex conjugate term to the loss function) and training area of the physics-informed neural network(PINN), the authors proposed two neural network models: Mix-training PINN and prior information mix-training PINN. The authors demonstrated the advantages of these models by simulating rogue waves in the nonlocal PT-symmetric Schr?dinger equation. Numerical experiments showed that the proposed models not only simulate first-order rogue waves, but also significantly improve the simulation capability. Compared with original PINN, the prediction accuracy of the first-order rouge waves are improved by one to three orders of magnitude. By testing the inverse problem of first-order rogue waves, it is also proved that these models have good performance.