Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEs
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Date
2020-06Type
- Report
ETH Bibliography
yes
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Abstract
Physics informed neural networks (PINNs) have recently been widely used for robust and accurate approximation of PDEs. We provide rigorous upper bounds on the generalization error of PINNs approximating solutions of the forward problem for PDEs. An abstract formalism is introduced and stability properties of the underlying PDE are leveraged to derive an estimate for the generalization error in terms of the training error and number of training samples. This abstract framework is illustrated with several examples of nonlinear PDEs. Numerical experiments, validating the proposed theory, are also presented. Show more
Publication status
publishedExternal links
Journal / series
SAM Research ReportVolume
Publisher
Seminar for Applied Mathematics, ETH ZurichSubject
PDE; Machine Learning; Numerical AnalysisOrganisational unit
03851 - Mishra, Siddhartha / Mishra, Siddhartha
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ETH Bibliography
yes
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