Error analysis for deep neural network approximations of parametric hyperbolic conservation laws
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Abstract (arXiv)
We derive rigorous bounds on the error resulting from the approximation of the solution of parametric hyperbolic scalar conservation laws with ReLU neural networks. We show that the approximation error can be made as small as desired with ReLU neural networks that overcome the curse of dimensionality. In addition, we provide an explicit upper bound on the generalization error in terms of the training error, number of training samples and the neural network size. The theoretical results are illustrated by numerical experiments.
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 17 of its 36 references that are in the map. First posted on arXiv 15 Jul 2022.
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17 of 36 references.
References · 17
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5 more
- 2020Iterative Surrogate Model Optimization (ISMO): An active learning algorithm for PDE constrained optimization with deep neural networkscited by 27
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Citing papers per year: 2022: 1; 2023: 1.
2 papers.