Low-rank cross approximation of vector-valued tensors with applications to parametric PDEs (Stanislav Budzinskiy, University of Vienna)

04.11.2025 14:00

Low-rank tensor decompositions are widely used to approximate multivariate functions with scalar values. Many practical implementations of this approach rely on low-rank cross approximation to build approximants based on function samples. In this talk, we will introduce the notion of Bochner tensors: multidimensional arrays whose entries are elements of a Hilbert space. These objects arise naturally in the context of parametric partial differential equations (PDEs) as discretisations of parameter-to-solution maps. We will generalise the Tucker format and the corresponding concept of cross approximation to Bochner tensors and illustrate the capability of this approach to construct reduced-order models of parametric PDEs in a purely data-driven manner with numerical experiments.

Lieu

Conseil Général 7-9, Room 1-05, Séminaire d'analyse numérique

entrée libre