Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEs II: A class of inverse problems
Metadata only
Date
2020-06Type
- Report
ETH Bibliography
yes
Altmetrics
Abstract
Physics informed neural networks (PINNs) have recently been very successfully applied for efficiently approximating inverse problems for PDEs. We focus on a particular class of inverse problems, the so-called data assimilation or unique continuation problems, and prove rigorous estimates on the generalization error of PINNs approximating them. An abstract framework is presented and conditional stability estimates for the underlying inverse problem are employed to derive the estimate on the PINN generalization error, providing rigorous justification for the use of PINNs in this context. The abstract framework is illustrated with examples of four prototypical linear 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; Numerical Analysis; Deep Learning; Inverse ProblemOrganisational unit
03851 - Mishra, Siddhartha / Mishra, Siddhartha
More
Show all metadata
ETH Bibliography
yes
Altmetrics