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Volume 39, Issue 6
Physics Informed Neural Networks (PINNs) For Approximating Nonlinear Dispersive PDEs

Genming Bai, Ujjwal Koley, Siddhartha Mishra & Roberto Molinaro

DOI: 10.4208/jcm.2101-m2020-0342

J. Comp. Math., 39 (2021), pp. 816-847.

Published online: 2021-10

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  • 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.

  • Keywords

Nonlinear dispersive PDEs, Deep learning, Physics Informed Neural Networks.

  • AMS Subject Headings

35Q53, 65M12, 65M15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

gbai@student.ethz.ch (Genming Bai)

ujjwal@math.tifrbng.res.in (Ujjwal Koley)

siddhartha.mishra@sam.math.ethz.ch (Siddhartha Mishra)

roberto.molinaro@sam.math.ethz.ch (Roberto Molinaro)

  • BibTex
  • RIS
  • TXT
@Article{JCM-39-816, author = {Bai , GenmingKoley , UjjwalMishra , Siddhartha and Molinaro , Roberto}, title = {Physics Informed Neural Networks (PINNs) For Approximating Nonlinear Dispersive PDEs}, journal = {Journal of Computational Mathematics}, year = {2021}, volume = {39}, number = {6}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2101-m2020-0342}, url = {http://global-sci.org/intro/article_detail/jcm/19913.html} }
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 -

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.

Bai , GenmingKoley , UjjwalMishra , Siddhartha and Molinaro , Roberto. (2021). Physics Informed Neural Networks (PINNs) For Approximating Nonlinear Dispersive PDEs. Journal of Computational Mathematics. 39 (6). 816-847. doi:10.4208/jcm.2101-m2020-0342
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