[HTML][HTML] Cross interpolation for solving high-dimensional dynamical systems on low-rank Tucker and tensor train manifolds

B Ghahremani, H Babaee - Computer Methods in Applied Mechanics and …, 2024 - Elsevier
We present a novel tensor interpolation algorithm for the time integration of nonlinear tensor
differential equations (TDEs) on the tensor train and Tucker tensor low-rank manifolds …

Cur for implicit time integration of random partial differential equations on low-rank matrix manifolds

MH Naderi, S Akhavan, H Babaee - arxiv preprint arxiv:2408.16591, 2024 - arxiv.org
Dynamical low-rank approximation allows for solving large-scale matrix differential
equations (MDEs) with significantly fewer degrees of freedom and has been applied to a …

A parallel Basis Update and Galerkin Integrator for Tree Tensor Networks

G Ceruti, J Kusch, C Lubich, D Sulz - arxiv preprint arxiv:2412.00858, 2024 - arxiv.org
Computing the numerical solution to high-dimensional tensor differential equations can lead
to prohibitive computational costs and memory requirements. To reduce the memory and …

A stable multiplicative dynamical low-rank discretization for the linear Boltzmann-BGK equation

L Baumann, L Einkemmer, C Klingenberg… - arxiv preprint arxiv …, 2024 - arxiv.org
The numerical method of dynamical low-rank approximation (DLRA) has recently been
applied to various kinetic equations showing a significant reduction of the computational …

Robust and conservative dynamical low-rank methods for the Vlasov equation via a novel macro-micro decomposition

J Coughlin, J Hu, U Shumlak - Journal of Computational Physics, 2024 - Elsevier
Dynamical low-rank (DLR) approximation has gained interest in recent years as a viable
solution to the curse of dimensionality in the numerical solution of kinetic equations …