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

Abstract

By the modifying loss function MSE and training area of physics-informed neural networks (PINNs), we propose a neural networks model, namely prior-information PINNs (PIPINNs). We demonstrate the advantages of PIPINNs by simulating Ai- and Bi-soliton solutions of the cylindrical Korteweg–de Vries (cKdV) equation. Numerical experiments show that our proposed model is able not only to simulate these solitons using the cKdV equation, but also to significantly improve its simulation capability. Compared with the original PINNs, the prediction accuracy of our proposed model is improved by one to three orders of magnitude. Moreover, the accuracy of the PIPINNs is further improved by adding the restriction of conservation of energy.