Physics Informed Neural Networks (PINNs) For Approximating Nonlinear Dispersive PDEs

Physics Informed Neural Networks (PINNs)  For Approximating Nonlinear Dispersive PDEs

Year:    2021

Author:    Genming Bai, Ujjwal Koley, Siddhartha Mishra, Roberto Molinaro

Journal of Computational Mathematics, Vol. 39 (2021), Iss. 6 : pp. 816–847

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2101-m2020-0342

Journal of Computational Mathematics, Vol. 39 (2021), Iss. 6 : pp. 816–847

Published online:    2021-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    32

Keywords:    Nonlinear dispersive PDEs Deep learning Physics Informed Neural Networks.

Author Details

Genming Bai

Ujjwal Koley

Siddhartha Mishra

Roberto Molinaro