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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Reduced order modeling inversion: From CalderÃ³n pr
oblem to SAR imaging - Vladimir Druskin (Worcester
Polytechnic Institute)
DTSTART;TZID=Europe/London:20230621T090000
DTEND;TZID=Europe/London:20230621T100000
UID:TALK200434AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/200434
DESCRIPTION:Reduced-order models (ROMs) have been proven to be
a useful tool for efficient simulations of the re
sponses of large-scale dynamical systems and their
identification. Here I focus on ROM&rsquo\;s appl
ications to the solution of the nonlinear inverse
coefficient problems for linear PDEs. Our framewor
k circumvents this nonlinearity by introducing a f
amily of recursive nonlinear data preprocessing pr
ocedures\, relying on sparse network realizations
of the data-driven (aka noninvasive) ROMs. This pr
ocedure &ldquo\;absorbs&rdquo\; much of the nonlin
earity of the problem\, thus making the subsequent
imaging or inversion a lot more straightforward.\
nThe uniqueness of Calderó\;n formulations w
as proven by several authors (the speaker included
) starting from the early 1980s\, however applicab
ility of the network approximations in this settin
g became only understood after works of de Verdier
e\, Curtis\, Ingerman and Morrow in the 1990s. I b
egin with the 1D inverse Sturm-Liouville problem a
nd estimate its electrical conductivity by embeddi
ng its network approximation. Then I outline gener
alizations of this approach for 2D Calderó\;
n formulations with complete and partial DtN data
using planar graphs and explain intrinsic difficul
ties for extensions to dimensions >2 due to curse
of dimensionality.\nFinally I present a ROM based
Lippmann-Schwinger inversion algorithm for wave pr
oblems and consider its application to the synthet
ic aperture radar (SAR) problem in a multiple-scat
tering environment\, which avoids the curse of dim
ensionality. The efficiency of this approach was r
ecently improved with the help of a novel data-com
pletion algorithm\, allowing to lift \; SAR (m
onostatic) data set to the multi-input/multi-outpu
t \; one.\nLiliana Borcea\, Fernando Guevara V
asquez\, David Ingerman\, Leonid Knizhnerman\, Ale
xander Mamonov\, Shari Moskow\, Andy Thaler\, Mikh
ail Zaslavskiy and Jö\;rn Zimmerling contribut
ed to different stages of this research.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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