| Autor: |
Hillebrecht, Birgit, Unger, Benjamin |
| Rok vydání: |
2022 |
| Předmět: |
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| Zdroj: |
IEEE Transactions on Neural Networks and Learning Systems (2023), 1-11 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1109/TNNLS.2023.3335837 |
| Popis: |
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 approaches. Beyond statistical investigations and generic results on the approximation capabilities of neural networks, we present a rigorous upper bound on the prediction error of physics-informed neural networks. This bound can be calculated without the knowledge of the true solution and only with a priori available information about the characteristics of the underlying dynamical system governed by a partial differential equation. We apply this a posteriori error bound exemplarily to four problems: the transport equation, the heat equation, the Navier-Stokes equation and the Klein-Gordon equation. |
| Databáze: |
arXiv |
| Externí odkaz: |
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