13 citations · 29 across the 7 of their papers we have counts for
8 papers
The fast reduced QMC matrix-vector product
Josef Dick, Adrian Ebert, Lukas Herrmann +2
We study the approximation of integrals , where is a matrix, by quasi-Monte Carlo (QMC) rules $N^{-1} \sum_{k=0}^{…
FakET: Simulating Cryo-Electron Tomograms with Neural Style Transfer
Pavol Harar, Lukas Herrmann, Philipp Grohs +1
In cryo-electron microscopy, accurate particle localization and classification are imperative. Recent deep learning solutions, though successful, require extensive training data se…
Analysis of RHC for stabilization of nonautonomous parabolic equations under uncertainty
Behzad Azmi, Lukas Herrmann, Karl Kunisch
Stabilization of a class of time-varying parabolic equations with uncertain input data using Receding Horizon Control (RHC) is investigated. The diffusion coefficient and the initi…
Neural and spectral operator surrogates: unified construction and expression rate bounds
Lukas Herrmann, Christoph Schwab, Jakob Zech
Approximation rates are analyzed for deep surrogates of maps between infinite-dimensional function spaces, arising e.g. as data-to-solution maps of linear and nonlinear partial dif…
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…
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…
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…
Numerical analysis of lognormal diffusions on the sphere
Lukas Herrmann, Annika Lang, Christoph Schwab
Numerical solutions of stationary diffusion equations on the unit sphere with isotropic lognormal diffusion coefficients are considered. Hölder regularity in sense for isotro…