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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
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
-
The Calderón’s Problem via DeepONets
Castro, Javier | Muñoz, Claudio | Valenzuela, NicolásVietnam Journal of Mathematics, Vol. 52 (2024), Iss. 3 P.775
https://doi.org/10.1007/s10013-023-00674-8 [Citations: 0] -
ERROR ESTIMATES OF RESIDUAL MINIMIZATION USING NEURAL NETWORKS FOR LINEAR PDES
Shin, Yeonjong | Zhang, Zhongqiang | Karniadakis, George EmJournal of Machine Learning for Modeling and Computing, Vol. 4 (2023), Iss. 4 P.73
https://doi.org/10.1615/JMachLearnModelComput.2023050411 [Citations: 13] -
Solution of One-Dimensional Stochastic Burgers Equation by Gradient-Enhanced Physics-Informed Neural Networks with Weak Noise
王, 蓉
Pure Mathematics, Vol. 14 (2024), Iss. 06 P.426
https://doi.org/10.12677/pm.2024.146261 [Citations: 0] -
Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs
De Ryck, Tim | Mishra, SiddharthaAdvances in Computational Mathematics, Vol. 48 (2022), Iss. 6
https://doi.org/10.1007/s10444-022-09985-9 [Citations: 36] -
Boundary-safe PINNs extension: Application to non-linear parabolic PDEs in counterparty credit risk
P. Villarino, Joel | Leitao, Álvaro | García Rodríguez, J.A.Journal of Computational and Applied Mathematics, Vol. 425 (2023), Iss. P.115041
https://doi.org/10.1016/j.cam.2022.115041 [Citations: 0] -
Physics-informed neural networks for approximating dynamic (hyperbolic) PDEs of second order in time: Error analysis and algorithms
Qian, Yanxia | Zhang, Yongchao | Huang, Yunqing | Dong, SuchuanJournal of Computational Physics, Vol. 495 (2023), Iss. P.112527
https://doi.org/10.1016/j.jcp.2023.112527 [Citations: 4] -
Error estimates for physics-informed neural networks approximating the Navier–Stokes equations
De Ryck, Tim | Jagtap, Ameya D | Mishra, SiddharthaIMA Journal of Numerical Analysis, Vol. 44 (2024), Iss. 1 P.83
https://doi.org/10.1093/imanum/drac085 [Citations: 32] -
Numerical Control: Part B
Nonoverlapping domain decomposition and virtual controls for optimal control problems of p-type on metric graphs
Leugering, Günter
2023
https://doi.org/10.1016/bs.hna.2022.11.002 [Citations: 0] -
Time difference physics-informed neural network for fractional water wave models
Liu, Wenkai | Liu, Yang | Li, HongResults in Applied Mathematics, Vol. 17 (2023), Iss. P.100347
https://doi.org/10.1016/j.rinam.2022.100347 [Citations: 6] -
Error assessment of an adaptive finite elements—neural networks method for an elliptic parametric PDE
Caboussat, Alexandre | Girardin, Maude | Picasso, MarcoComputer Methods in Applied Mechanics and Engineering, Vol. 421 (2024), Iss. P.116784
https://doi.org/10.1016/j.cma.2024.116784 [Citations: 0]