Error Estimates for Neural Network Solutions of Partial Differential Equations

Piotr Minakowski, Thomas Richter

We develop an error estimator for neural network approximations of PDEs. The proposed approach is based on dual weighted residual estimator (DWR). It is destined to serve as a stopping criterion that guarantees the accuracy of the solution independently of the design of the neural network training. The result is equipped with computational examples for Laplace and Stokes problems.

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