For well-posed variational problems, the error of any approximation, including a neural network, is equivalent to the sum of a computable discrete residual and an estimated remainder.
Finite element interpolated neural networks for solving forward and inverse problems
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A posteriori analysis of neural network approximations
For well-posed variational problems, the error of any approximation, including a neural network, is equivalent to the sum of a computable discrete residual and an estimated remainder.