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Aspects of adaptive Galerkin FE for stochastic direct and inverse problems

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UNQW02 - Surrogate models for UQ in complex systems

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 parameter 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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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