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

2021/04/12 by Genming Bai, Ujjwal Koley, Bai, Genming +5 · 1 citation
Computer Science · Earth and Planetary Sciences · Engineering · Mathematics · Physics and Astronomy · #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Meteorological Phenomena and Simulations #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #cs.NA #math.NA

paper · pdf · doi:10.48550/arxiv.2104.05584

arXiv admin note: text overlap with arXiv:2006.16144

openalex publication_date 2021/04/12 · arxiv created 2022/05/18 · arxiv updated 2022/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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

Citations

• The Korteweg–de Vries–Kawahara equation in a bounded domain and some numerical results
• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data
• Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems
• Fourier Neural Operator for Parametric Partial Differential Equations
• Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEs

Cited by

• PINN-DG: Residual neural network methods trained with Finite Elements
• A residual weighted physics informed neural network for forward and inverse problems of reaction diffusion equations

Related

• Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEs
• Error analysis for physics informed neural networks (PINNs) approximating Kolmogorov PDEs
• Physics Informed Neural Networks (PINNs) as intelligent computing technique for solving partial differential equations: Limitation and Future prospects
• Numerical Approximations of the Allen-Cahn-Ohta-Kawasaki (ACOK) Equation with Modified Physics Informed Neural Networks (PINNs)
• VS-PINN: A fast and efficient training of physics-informed neural networks using variable-scaling methods for solving PDEs with stiff behavior