most citedMultilevel approximation of Gaussian random fields: Covariance compression, estimation and spatial prediction

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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.NA2020

Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions

Philipp Grohs, Lukas Herrmann

In recent work it has been established that deep neural networks are capable of approximating solutions to a large class of parabolic partial differential equations without incurri…