Physics Informed Neural Networks (PINNs)for approximating nonlinear dispersive PDEs

Genming Bai; Roberto Molinaro; Siddhartha Mishra; Ujjwal Koley

Physics Informed Neural Networks (PINNs)for approximating nonlinear dispersive PDEs

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arxiv 2104.05584 v2 pith:BWAFUGXE submitted 2021-04-12 math.NA cs.NA

Genming Bai , Ujjwal Koley , Siddhartha Mishra , Roberto Molinaro This is my paper · ORCID

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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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PINN-DG: Residual neural network methods trained with Finite Elements
math.NA 2025-07 conditional novelty 5.0 of 10

PINN-DG replaces pointwise derivative losses with finite element interpolation plus discontinuous Galerkin consistency and penalty terms, and proves convergence of the discrete minimizers.

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