5 citations · 6 across the 2 of their papers we have counts for
3 papers
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.ST2021★ 5 cited
Multilevel approximation of Gaussian random fields: Covariance compression, estimation and spatial prediction
Helmut Harbrecht, Lukas Herrmann, Kristin Kirchner +1
Centered Gaussian random fields (GRFs) indexed by compacta such as smooth, bounded Euclidean domains or smooth, compact and orientable manifolds are determined by their covariance…
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…