TY - JOUR
T1 - Physics Informed Neural Networks (PINNs)  For Approximating Nonlinear Dispersive PDEs
AU - Bai , Genming
AU - Koley , Ujjwal
AU - Mishra , Siddhartha
AU - Molinaro , Roberto
JO - Journal of Computational Mathematics
VL - 6
SP - 816
EP - 847
PY - 2021
DA - 2021/10
SN - 39
DO - http://doi.org/10.4208/jcm.2101-m2020-0342
UR - https://global-sci.org/intro/article_detail/jcm/19913.html
KW - Nonlinear dispersive PDEs, Deep learning, Physics Informed Neural Networks.
AB - <p style="text-align: justify;">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.</p>