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.