358 citations · 807 across the 21 of their papers we have counts for
4 papers · 1 filter
Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor representations
Martin Eigel, Manuel Marschall, Max Pfeffer +1
Stochastic Galerkin methods for non-affine coefficient representations are known to cause major difficulties from theoretical and numerical points of view. In this work, an adaptiv…
Variational Monte Carlo - Bridging Concepts of Machine Learning and High Dimensional Partial Differential Equations
Martin Eigel, Reinhold Schneider, Philipp Trunschke +1
A statistical learning approach for parametric PDEs related to Uncertainty Quantification is derived. The method is based on the minimization of an empirical risk on a selected mod…
Numerical and Theoretical Aspects of the DMRG-TCC Method Exemplified by the Nitrogen Dimer
Fabian M. Faulstich, Mihály Máté, Andre Laestadius +8
In this article, we investigate the numerical and theoretical aspects of the coupled-cluster method tailored by matrix-product states. We investigate chemical properties of the use…
Analysis of The Tailored Coupled-Cluster Method in Quantum Chemistry
Fabian M. Faulstich, Andre Laestadius, Örs Legeza +2
In quantum chemistry, one of the most important challenges is the static correlation problem when solving the electronic Schrödinger equation for molecules in the Born--Oppenheimer…