Error estimates for physics informed neural networks approximating the\n Navier-Stokes equations

2022/03/17 by Tim De Ryck, Ameya D. Jagtap, De Ryck, Tim +3 · 10 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Artificial intelligence #Artificial neural network #Compressibility #Computer science #Error analysis #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning and ELM #Mathematics #Model Reduction and Neural Networks #Navier–Stokes equations #Neural Networks and Applications #Numerical Analysis (math.NA) #Physics #Quadrature (astronomy) #Residual

paper · pdf · doi:10.48550/arxiv.2203.09346

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2022/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove rigorous bounds on the errors resulting from the approximation of\nthe incompressible Navier-Stokes equations with (extended) physics informed\nneural networks. We show that the underlying PDE residual can be made\narbitrarily small for tanh neural networks with two hidden layers. Moreover,\nthe total error can be estimated in terms of the training error, network size\nand number of quadrature points. The theory is illustrated with numerical\nexperiments.\n

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