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- Title
Error estimates for physics-informed neural networks approximating the Navier–Stokes equations.
- Authors
Ryck, Tim De; Jagtap, Ameya D; Mishra, Siddhartha
- Abstract
We prove rigorous bounds on the errors resulting from the approximation of the incompressible Navier–Stokes equations with (extended) physics-informed neural networks. We show that the underlying partial differential equation residual can be made arbitrarily small for tanh neural networks with two hidden layers. Moreover, the total error can be estimated in terms of the training error, network size and number of quadrature points. The theory is illustrated with numerical experiments.
- Publication
IMA Journal of Numerical Analysis, 2024, Vol 44, Issue 1, p83
- ISSN
0272-4979
- Publication type
Article
- DOI
10.1093/imanum/drac085