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SUMMARY:Shari Moskow (Drexel University)
DTSTART:20200528T160000Z
DTEND:20200528T170000Z
DTSTAMP:20260423T021130Z
UID:Inverse/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Inverse/2/">
 Reduced order models for spectral domain inversion: embedding into the con
 tinuous problem and generation of internal data</a>\nby Shari Moskow (Drex
 el University) as part of International Zoom Inverse Problems Seminar\, UC
  Irvine\n\n\nAbstract\nWe generate data-driven reduced order models (ROMs)
  for inversion of the\none and two dimensional Schrodinger equation in th
 e spectral domain given boundary data\nat a few frequencies. The ROM is th
 e Galerkin projection of the Schrodinger operator onto\nthe space spanned
  by solutions at these sample frequencies. The ROM matrix is in general\nf
 ull\, and not good for extracting the potential. However\, using an orthog
 onal change of\nbasis via Lanczos iteration\, we can transform the ROM to 
 a block triadiagonal form from\nwhich it is easier to extract q. In one di
 mension\, the tridiagonal matrix corresponds to\na three-point staggered f
 inite difference system for the Schrodinger operator discretized\non a so
 -called spectrally matched grid which is almost independent of the medium.
  In\nhigher dimensions\, the orthogonalized basis functions play the role 
 of the grid steps. The\northogonalized basis functions are localized and a
 lso depend only very weakly on the\nmedium\, and thus by embedding into th
 e continuous problem\, the reduced order model\nyields highly accurate int
 ernal solutions. That is to say\, we can obtain\, just from boundary\ndata
 \, very good approximations of the solution of the Schrodinger equation i
 n the whole\ndomain for a spectral interval that includes the sample frequ
 encies. We present inversion\nexperiments based on the internal solutions 
 in one and two dimensions.\n\n*joint with L. BORCEA\, V. DRUSKIN\, A. MAMO
 NOV\,  M. ZASLAVSKY\n
LOCATION:https://researchseminars.org/talk/Inverse/2/
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