Data-Driven Rogue Waves in Nonlocal PT-Symmetric Schrödinger Equation via Mix-Training PINN

• Published in: Journal of systems science and complexity Vol. 38; no. 5; pp. 2272 - 2290
• Main Authors: Sun, Jiawei, Li, Biao
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2025; Springer Nature B.V
• Subjects: Complex Systems; Control; Inverse problems; Mathematics; Mathematics and Statistics; Mathematics of Computing; Neural networks; Operations Research/Decision Theory; Schrodinger equation; Statistics; Systems Theory; physics-informed neural network; rogue waves; nonlocal NLS equation; Mix-training; prior information
• ISSN: 1009-6124; 1559-7067
• DOI: 10.1007/s11424-024-3418-3

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 P T -symmetric Schrödinger 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.