Error estimates for physics informed neural networks approximating the Navier-Stokes equations
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Date
2022-03Type
- Report
ETH Bibliography
yes
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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 PDE 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. Show more
Publication status
publishedExternal links
Journal / series
SAM Research ReportVolume
Publisher
Seminar for Applied Mathematics, ETH ZurichOrganisational unit
03851 - Mishra, Siddhartha / Mishra, Siddhartha
Related publications and datasets
Is previous version of: http://hdl.handle.net/20.500.11850/596774
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ETH Bibliography
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