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20162026
most citedA proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients

48 citations · 151 across the 14 of their papers we have counts for

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Showing 2018Show all

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math.CA2018★ 1 cited

Existence and uniqueness properties for solutions of a class of Banach space valued evolution equations

Arnulf Jentzen, Sara Mazzonetto, Diyora Salimova

In this note we provide a self-contained proof of an existence and uniqueness result for a class of Banach space valued evolution equations with an additive forcing term. The frame…

math.NA2018★ 48 cited

A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients

Arnulf Jentzen, Diyora Salimova, Timo Welti

In recent years deep artificial neural networks (DNNs) have been successfully employed in numerical simulations for a multitude of computational problems including, for example, ob…