Physics Informed Neural Networks (PINNs)for approximating nonlinear dispersive PDEs
Numerical Analysis
2022-05-19 v2 Numerical Analysis
Abstract
We propose a novel algorithm, based on physics-informed neural networks (PINNs) to efficiently approximate solutions of nonlinear dispersive PDEs such as the KdV-Kawahara, Camassa-Holm and Benjamin-Ono equations. The stability of solutions of these dispersive PDEs is leveraged to prove rigorous bounds on the resulting error. We present several numerical experiments to demonstrate that PINNs can approximate solutions of these dispersive PDEs very accurately
Cite
@article{arxiv.2104.05584,
title = {Physics Informed Neural Networks (PINNs)for approximating nonlinear dispersive PDEs},
author = {Genming Bai and Ujjwal Koley and Siddhartha Mishra and Roberto Molinaro},
journal= {arXiv preprint arXiv:2104.05584},
year = {2022}
}
Comments
arXiv admin note: text overlap with arXiv:2006.16144