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SUMMARY:Reduced order modeling inversion: From Calderón problem to SAR im
 aging - Vladimir Druskin (Worcester Polytechnic Institute)
DTSTART:20230621T080000Z
DTEND:20230621T090000Z
UID:TALK200434@talks.cam.ac.uk
DESCRIPTION:Reduced-order models (ROMs) have been proven to be a useful to
 ol for efficient simulations of the responses of large-scale dynamical sys
 tems and their identification. Here I focus on ROM&rsquo\;s applications t
 o the solution of the nonlinear inverse coefficient problems for linear PD
 Es. Our framework circumvents this nonlinearity by introducing a family of
  recursive nonlinear data preprocessing procedures\, relying on sparse net
 work realizations of the data-driven (aka noninvasive) ROMs. This procedur
 e &ldquo\;absorbs&rdquo\; much of the nonlinearity of the problem\, thus m
 aking the subsequent imaging or inversion a lot more straightforward.\nThe
  uniqueness of Calder&oacute\;n formulations was proven by several authors
  (the speaker included) starting from the early 1980s\, however applicabil
 ity of the network approximations in this setting became only understood a
 fter works of de Verdiere\, Curtis\, Ingerman and Morrow in the 1990s. I b
 egin with the 1D inverse Sturm-Liouville problem and estimate its electric
 al conductivity by embedding its network approximation. Then I outline gen
 eralizations of this approach for 2D Calder&oacute\;n formulations with co
 mplete and partial DtN data using planar graphs and explain intrinsic diff
 iculties for extensions to dimensions >2 due to curse of dimensionality.\n
 Finally I present a ROM based Lippmann-Schwinger inversion algorithm for w
 ave problems and consider its application to the synthetic aperture radar 
 (SAR) problem in a multiple-scattering environment\, which avoids the curs
 e of dimensionality. The efficiency of this approach was recently improved
  with the help of a novel data-completion algorithm\, allowing to lift&nbs
 p\; SAR (monostatic) data set to the multi-input/multi-output&nbsp\; one.\
 nLiliana Borcea\, Fernando Guevara Vasquez\, David Ingerman\, Leonid Knizh
 nerman\, Alexander Mamonov\, Shari Moskow\, Andy Thaler\, Mikhail Zaslavsk
 iy and J&ouml\;rn Zimmerling contributed to different stages of this resea
 rch.
LOCATION:Seminar Room 1\, Newton Institute
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