Error estimates of deep learning methods for the nonstationary Magneto-hydrodynamics equations

Abstract

In this study, we prove rigourous bounds on the error and stability analysis of deep learning methods for the nonstationary Magneto-hydrodynamics equations. We obtain the approximate ability of the neural network by the convergence of a loss function and the convergence of a Deep Neural Network (DNN) to the exact solution. Moreover, we derive explicit error estimates for the solution computed by optimizing the loss function in the DNN approximation of the solution.