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SUMMARY:Aspects of adaptive Galerkin FE for stochastic direct and inverse 
 problems - Martin  Eigel (Weierstraß-Institut für Angewandte Analysis un
 d Stochastik)
DTSTART:20180207T090000Z
DTEND:20180207T100000Z
UID:TALK100102@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>Co-authors: Max Pfeffer		(MPI MIS Leipzig)\, Manuel Mars
 chall		(WIAS Berlin)\, Reinhold Schneider		(TU Berlin)        <br></span><
 span><br>The Stochastic Galerkin Finite Element Method (SGFEM) is a common
  approach to numerically solve random PDEs with the aim to obtain a functi
 onal representation of the stochastic solution. As with any spectral metho
 d\, the curse of dimensionality renders the approach challenging when the 
 randomness depends on a large or countable infinite set of parameters. Thi
 s makes function space adaptation and model reduction strategies a necessi
 ty. We review adaptive SGFEM based on reliable a posteriori error estimato
 rs 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 statistic
 al learning viewpoint is presented\, which connects concepts of UQ and mac
 hine learning from a Variational Monte Carlo perspective.</span>
LOCATION:Seminar Room 1\, Newton Institute
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