Research reports

On generalization error estimates of physics informed neural networks for approximating dispersive PDEs

by G. Bai and U. Koley and S. Mishra and R. Molinaro

(Report number 2021-13)

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 several dispersive PDEs.

Keywords: Deep Learning; Physics Informed Neural Networks (PINNs); Dispersive PDEs;

BibTeX
@Techreport{BKMM21_955,
  author = {G. Bai and U. Koley and S. Mishra and R. Molinaro},
  title = {On generalization error estimates of physics informed neural networks for approximating dispersive PDEs},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2021-13},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2021/2021-13.pdf },
  year = {2021}
}

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