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 (DNN) approximation of the solution, with a fixed complexity.
@article{arxiv.2008.02844,
title = {Error Estimates for Deep Learning Methods in Fluid Dynamics},
author = {Animikh Biswas and Jing Tian and Suleyman Ulusoy},
journal= {arXiv preprint arXiv:2008.02844},
year = {2020}
}