Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEs II: A class of inverse problems.
Published: Jun 29, 2020
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...
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