11 papers
Iterative thresholding low-rank time integration for high-dimensional problems
Markus Bachmayr, Tianyu Jin, Polina Sachsenmaier +1
This work analyzes a method for time integration of high-dimensional linear Schrödinger-type problems based on hierarchical tensor approximations. In particular, this method provid…
Low-rank eigenvalue solvers for block-sparse matrix product states
Markus Bachmayr, Sebastian Krämer, Max Pfeffer
We consider an iterative eigensolver for Schrödinger equations that constructs low-rank approximations of eigenfunctions with accuracy-adapted ranks, with particular focus on ferm…
Preconditioning and Numerical Stability in Neural Network Training for Parametric PDEs
Markus Bachmayr, Wolfgang Dahmen, Chenguang Duan +1
In the context of training neural network-based approximations of solutions of parameter-dependent PDEs, we investigate the effect of preconditioning via well-conditioned frame rep…
Fluid flow channeling and mass transport with discontinuous porosity distribution
Simon Boisserée, Evangelos Moulas, Markus Bachmayr
The flow of fluids within porous rocks is an important process with numerous applications in Earth sciences. Modeling the compaction-driven fluid flow requires the solution of coup…
An adaptive space-time method for nonlinear poroviscoelastic flows with discontinuous porosities
Markus Bachmayr, Simon Boisserée
This paper is concerned with a space-time adaptive numerical method for instationary porous media flows with nonlinear interaction between porosity and pressure, with focus on prob…
Iterative thresholding low-rank time integration
Markus Bachmayr, Matthieu Dolbeault, Polina Sachsenmaier
We develop time integration methods in low-rank representation that can adaptively adjust approximation ranks to achieve a prescribed accuracy, while ensuring that these ranks rema…