12 citations · 15 across the 4 of their papers we have counts for
4 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}^{…
A-posteriori QMC-FEM error estimation for Bayesian inversion and optimal control with entropic risk measure
Marcello Longo, Christoph Schwab, Andreas Stein
We propose a novel a-posteriori error estimation technique where the target quantities of interest are ratios of high-dimensional integrals, as occur e.g. in PDE constrained Bayesi…
De Rham compatible Deep Neural Network FEM
Marcello Longo, Joost A. A. Opschoor, Nico Disch +2
On general regular simplicial partitions of bounded polytopal domains , , we construct \emph{exact neural network (NN) emulations}…
Higher-order Quasi-Monte Carlo Training of Deep Neural Networks
M. Longo, S. Mishra, T. K. Rusch +1
We present a novel algorithmic approach and an error analysis leveraging Quasi-Monte Carlo points for training deep neural network (DNN) surrogates of Data-to-Observable (DtO) maps…