624	RWTH Publication No: 974379        2023
TITLE	Dynamical low-rank tensor approximations to high-dimensional parabolic problems: existence and convergence of spatial discretizations
AUTHORS	Markus Bachmayr, Henrik Eisenmann, André Uschmajew
ABSTRACT	We consider dynamical low-rank approximations to parabolic problems on higher-order tensor manifolds in Hilbert spaces. In addition to existence of solutions and their stability with respect to perturbations to the problem data, we show convergence of spatial discretizations. Our framework accommodates various standard low-rank tensor formats for multivariate functions, including tensor train and hierarchical tensors.
KEYWORDS	low-rank approximation, tensor train, hierarchical tensors