Biswas, AnimikhTian, JingUlusoy, Suleyman2020-09-112020-09-112022-05-31Biswas, 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-zhttps://doi.org/10.1007/s00211-022-01294-zIn 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.25 pagesen-USThis 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.Public Domain Mark 1.0https://creativecommons.org/publicdomain/mark/1.0/Text