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SUMMARY:Joint-sparse recovery for high-dimensional parametric PDEs - Nicho
 las Dexter (University of Tennessee\; Oak Ridge National Laboratory)
DTSTART:20180412T100000Z
DTEND:20180412T103000Z
UID:TALK103972@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Co-authors: Hoang Tran (Oak Ridge National Laboratory) & Clayt
 on Webster (University of Tennessee & Oak Ridge National Laboratory)  We p
 resent and analyze a novel sparse polynomial approximation method for the 
 solution of PDEs with stochastic and parametric inputs. Our approach treat
 s the parameterized problem as a problem of joint-sparse signal recovery\,
  i.e.\, simultaneous reconstruction of a set of sparse signals\, sharing a
  common sparsity pattern\, from a countable\, possibly infinite\, set of m
 easurements. In this setting\, the support set of the signal is assumed to
  be unknown and the measurements may be corrupted by noise. We propose the
  solution of a linear inverse problem via convex sparse regularization for
  an approximation to the true signal. Our approach allows for global appro
 ximations of the solution over both physical and parametric domains. In ad
 dition\, we show that the method enjoys the minimal sample complexity requ
 irements common to compressed sensing-based approaches. We then perform ex
 tensive numerical experiments on several high-dimensional parameterized el
 liptic PDE models to demonstrate the recovery properties of the proposed a
 pproach.
LOCATION:Seminar Room 1\, Newton Institute
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