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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Joint-sparse recovery for high-dimensional paramet
ric PDEs - Nicholas Dexter (University of Tennesse
e\; Oak Ridge National Laboratory)
DTSTART;TZID=Europe/London:20180412T110000
DTEND;TZID=Europe/London:20180412T113000
UID:TALK103972AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/103972
DESCRIPTION:Co-authors: Hoang Tran (Oak Ridge National Laborat
ory) & Clayton Webster (University of Tennessee &
Oak Ridge National Laboratory) We present and ana
lyze a novel sparse polynomial approximation metho
d for the solution of PDEs with stochastic and par
ametric inputs. Our approach treats the parameteri
zed problem as a problem of joint-sparse signal re
covery\, i.e.\, simultaneous reconstruction of a s
et of sparse signals\, sharing a common sparsity p
attern\, from a countable\, possibly infinite\, se
t of measurements. In this setting\, the support s
et 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 conv
ex sparse regularization for an approximation to t
he true signal. Our approach allows for global app
roximations of the solution over both physical and
parametric domains. In addition\, we show that th
e method enjoys the minimal sample complexity requ
irements common to compressed sensing-based approa
ches. We then perform extensive numerical experime
nts on several high-dimensional parameterized elli
ptic PDE models to demonstrate the recovery proper
ties of the proposed approach.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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