Physics Informed Neural Networks (PINNs) For Approximating Nonlinear Dispersive PDEs (Journal of Computational Mathematics, 2021)
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.
Keywords: Nonlinear dispersive PDEs; Deep learning; Physics Informed Neural Networks.