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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:TALK103969@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Co-authors: Hoang Tran (Oak Ridge National Laboratory) &amp\; 
 Clayton Webster (University of Tennessee &amp\; Oak Ridge National Laborat
 ory)  We present and analyze a novel sparse polynomial approximation metho
 d for the solution of PDEs with stochastic and parametric inputs. Our appr
 oach treats 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 measurements. In this setting\, the support set of the signal is 
 assumed to be unknown and the measurements may be corrupted by noise. We p
 ropose the solution of a linear inverse problem via convex sparse regulari
 zation for an approximation to the true signal. Our approach allows for gl
 obal approximations of the solution over both physical and parametric doma
 ins. In addition\, we show that the method enjoys the minimal sample compl
 exity requirements common to compressed sensing-based approaches. We then 
 perform extensive numerical experiments on several high-dimensional parame
 terized elliptic PDE models to demonstrate the recovery properties of the 
 proposed approach.
LOCATION:Seminar Room 1\, Newton Institute
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