Preprint

Deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear partial differential equations



Publication Details
Authors:
Cioica-Licht, P.; Hutzenthaler, M.; Werner, P.

Publication year:
2022
Journal:
arXiv Preprint
Pages range :
1-34
Journal acronym:
arXiv
DOI-Link der Erstveröffentlichung:


Abstract
We prove that deep neural networks are capable of approximating solutions of semilinear Kolmogorov PDE in the case of gradient-independent, Lipschitz-continuous nonlinearities, while the required number of parameters in the networks grow at most polynomially in both dimension {\$}d $\backslash$in \mathbbN{\$} and prescribed reciprocal accuracy {\$}$\backslash$varepsilon{\$}. Previously, this has only been proven in the case of semilinear heat equations.


Authors/Editors

Last updated on 2023-16-06 at 14:09