Error Estimates for Deep Learning Methods in Fluid Dynamics

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https://link.springer.com/article/10.1007/s00211-022-01294-z

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https://doi.org/10.1007/s00211-022-01294-z

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UMBC Mathematics and Statistics Department
UMBC Faculty Collection

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Author/Creator ORCID

https://orcid.org/0000-0001-8594-0568

Date

2022-05-31

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journal articles
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Citation of Original Publication

Biswas, A., Tian, J. & Ulusoy, S. Error estimates for deep learning methods in fluid dynamics. Numer. Math. 151, 753–777 (2022). https://doi.org/10.1007/s00211-022-01294-z

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This is a work of the United States Government. In accordance with 17 U.S.C. 105, no copyright protection is available for such works under U.S. Law.
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https://creativecommons.org/publicdomain/mark/1.0/

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Abstract

In this study, we provide error estimates and stability analysis of deep learning techniques for certain partial differential equations including the incompressible Navier–Stokes equations. In particular, we obtain explicit error estimates (in suitable norms) for the solution computed by optimizing a loss function in a Deep Neural Network approximation of the solution, with a fixed complexity.