Dynamical low-rank approximation for parabolic problems

André Uschmajew (MPI Leipzig)

May 09. 2022, 11:20 — 12:10

Dynamical low-rank approximation is a framework for time integration of matrix valued ODEs on a fixed-rank manifold based on a time dependent variational principle. Several applications arise from PDEs on product domains, but setting up a corresponding well-posed problem in function space (before discretization) may not be straightforward. Here we present a weak formulation of dynamical low-rank approximation for parabolic PDEs in two spatial dimensions. The existence and uniqueness of weak solutions is shown using a variational time-stepping scheme on the low-rank manifold which is related to practical methods for low-rank integration.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Associated Event:
Computational Uncertainty Quantification: Mathematical Foundations, Methodology & Data (Thematic Programme)
Organizer(s):
Clemens Heitzinger (TU Vienna)
Fabio Nobile (EPFL Lausanne)
Robert Scheichl (U Heidelberg)
Christoph Schwab (ETH Zürich)
Sara van de Geer (ETH Zürich)
Karen Willcox (U of Texas, Austin)