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20092023
most citedA proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations

153 citations · 899 across the 45 of their papers we have counts for

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Showing 2021 · math.NAShow all

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math.NA2021★ 1 cited

Deep neural network approximation for high-dimensional parabolic Hamilton-Jacobi-Bellman equations

Philipp Grohs, Lukas Herrmann

The approximation of solutions to second order Hamilton--Jacobi--Bellman (HJB) equations by deep neural networks is investigated. It is shown that for HJB equations that arise in t…

math.NA2021★ 1 cited

Lower bounds for artificial neural network approximations: A proof that shallow neural networks fail to overcome the curse of dimensionality

Philipp Grohs, Shokhrukh Ibragimov, Arnulf Jentzen +1

Artificial neural networks (ANNs) have become a very powerful tool in the approximation of high-dimensional functions. Especially, deep ANNs, consisting of a large number of hidden…