Error Estimates for Neural Network Solutions of Partial Differential Equations

07/23/2021
by   Piotr Minakowski, et al.
0

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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