5 papers · 1 filter
On low-rank tensor train approximability for linear nearest neighbor systems
Patrick Gelß, Sebastian Matera, Reinhold Schneider +1
Low-rank tensor methods are an important tool in the numerical treatment of equations with a high-dimensional state space. Nearest neighbor interaction systems like the Ising model…
A block-sparse Tensor Train Format for sample-efficient high-dimensional Polynomial Regression
Michael Götte, Reinhold Schneider, Philipp Trunschke
Low-rank tensors are an established framework for high-dimensional least-squares problems. We propose to extend this framework by including the concept of block-sparsity. In the co…
Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks
Moritz Geist, Philipp Petersen, Mones Raslan +2
We perform a comprehensive numerical study of the effect of approximation-theoretical results for neural networks on practical learning problems in the context of numerical analysi…
A Theoretical Analysis of Deep Neural Networks and Parametric PDEs
Gitta Kutyniok, Philipp Petersen, Mones Raslan +1
We derive upper bounds on the complexity of ReLU neural networks approximating the solution maps of parametric partial differential equations. In particular, without any knowledge…
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…