4 citations · 4 across the 3 of their papers we have counts for
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Deep neural network approximation theory for high-dimensional functions
Pierfrancesco Beneventano, Patrick Cheridito, Robin Graeber +2
The purpose of this article is to develop a machinery to study the capacity of deep neural networks (DNNs) to approximate high-dimensional functions. In particular, we show that DN…
Deep learning based numerical approximation algorithms for stochastic partial differential equations
Christian Beck, Sebastian Becker, Patrick Cheridito +2
In this article, we introduce and analyze a deep learning based approximation algorithm for SPDEs. Our approach employs neural networks to approximate the solutions of SPDEs along…
High-dimensional approximation spaces of artificial neural networks and applications to partial differential equations
Pierfrancesco Beneventano, Patrick Cheridito, Arnulf Jentzen +1
In this paper we develop a new machinery to study the capacity of artificial neural networks (ANNs) to approximate high-dimensional functions without suffering from the curse of di…