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cs.LG2022★ 6 cited
Certified machine learning: Rigorous a posteriori error bounds for PDE defined PINNs
Birgit Hillebrecht, Benjamin Unger
Prediction error quantification in machine learning has been left out of most methodological investigations of neural networks, for both purely data-driven and physics-informed app…
cs.LG2022★ 11 cited
Certified machine learning: A posteriori error estimation for physics-informed neural networks
Birgit Hillebrecht, Benjamin Unger
Physics-informed neural networks (PINNs) are one popular approach to incorporate a priori knowledge about physical systems into the learning framework. PINNs are known to be robust…