Data-Driven Ai- and Bi-Soliton of the Cylindrical Korteweg–de Vries Equation via Prior-Information Physics-Informed Neural Networks

Abstract

In this paper, by modifying loss function MS E and training area of the physics-informed neural networks (PINNs), we proposed a neural networks models: prior information PINNs (PIPINNs). We demonstrated the advantages of PIPINNs by simulating Ai- and Bi-soliton solutions of the cylindrical Korteweg-de Vries (cKdV) equation. Numerical experiments showed that our proposed model is not only simulate these solitons of cKdV equation, but also significantly improve the simulation capability. Compared with original PINNs, the prediction accuracy of our proposed models are improved by one to three orders of magnitude. Moreover, the accuracy of PIPINNs is improved again by adding the restriction of conservation of energy.