arXiv (OAI Expanded)
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Trustworthy AI in numerics: On verification algorithms for neural network-based PDE solvers
We present new algorithms for a posteriori verification of neural networks (NNs) approximating solutions to PDEs. We use numerical quadrature to compute upper bounds for $L^2$ norms of NNs and their derivatives. When combined with energy estimates for specific PDEs, this yields verification algorith
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