skip to content

Aspects of adaptive Galerkin FE for stochastic direct and inverse problems

Presented by: 
Martin Eigel Weierstraß-Institut für Angewandte Analysis und Stochastik
Wednesday 7th February 2018 - 09:00 to 10:00
INI Seminar Room 1
Co-authors: Max Pfeffer (MPI MIS Leipzig), Manuel Marschall (WIAS Berlin), Reinhold Schneider (TU Berlin)

The Stochastic Galerkin Finite Element Method (SGFEM) is a common approach to numerically solve random PDEs with the aim to obtain a functional representation of the stochastic solution. As with any spectral method, the curse of dimensionality renders the approach challenging when the randomness depends on a large or countable infinite set of parameters. This makes function space adaptation and model reduction strategies a necessity. We review adaptive SGFEM based on reliable a posteriori error estimators for affine and non-affine parametric representations. Based on this, an adaptive explicit sampling-free Bayesian inversion in hierarchical tensor formats can be derived. As an outlook onto current research, a statistical learning viewpoint is presented, which connects concepts of UQ and machine learning from a Variational Monte Carlo perspective.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons