33 citations · 62 across the 26 of their papers we have counts for
35 papers
Efficient localised model reduction for multiscale PDEs via Grassmannian interpolation
Christian Alber, Markus Bachmayr, Robert Scheichl +1
Multiscale, parameter-dependent partial differential equations (PDEs) pose severe computational challenges due to strong coefficient heterogeneity and high-dimensional parameter sp…
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 fermi…
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…
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…
Sparse and low-rank approximations of parametric elliptic PDEs: the best of both worlds
Markus Bachmayr, Huqing Yang
A new approximation format for solutions of partial differential equations depending on infinitely many parameters is introduced. By combining low-rank tensor approximation in a se…