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SUMMARY:Rothschild Lecture: When data driven reduced order modeling meets 
 full waveform inversion - Liliana Borcea (University of Michigan)
DTSTART:20230524T150000Z
DTEND:20230524T160000Z
UID:TALK200230@talks.cam.ac.uk
DESCRIPTION:This talk is concerned with the following inverse problem for 
 the wave equation: Determine the variable\nwave speed from data gathered b
 y a collection of sensors\, which emit probing signals and measure the&nbs
 p\;\ngenerated backscattered waves. Inverse backscattering is an interdisc
 iplinary field driven by applications in geophysical\nexploration\, radar 
 imaging\, non-destructive evaluation of materials\, etc. There are two typ
 es of methods:\n(1) Qualitative (imaging) methods\, which address the simp
 ler problem of locating reflective structures in a known host medium.&nbsp
 \;\n(2) Quantitative methods\, also known as velocity estimation.&nbsp\;\n
 Typically\, velocity estimation is &nbsp\;formulated as a PDE constrained 
 optimization\, where the data are fit in the least squares\nsense by the w
 ave computed at the search wave speed. The increase in computing power has
  lead to growing interest\nin this approach\, but there is a fundamental i
 mpediment\, which manifests especially for high frequency data: The object
 ive function&nbsp\;is not convex and has numerous local minima even in the
  absence of noise. The main goal of the talk is to introduce a novel appro
 ach&nbsp\;to velocity estimation\, based on a reduced order model (ROM) of
  the wave operator. The ROM is called data driven because it is obtained&n
 bsp\;from the measurements made at the sensors. The mapping between these 
 measurements and the ROM is nonlinear\, and yet the ROM can be computed ef
 ficiently using methods from numerical linear algebra. More importantly\,&
 nbsp\;the ROM can be used to define a better objective function for veloci
 ty estimation\, so that gradient based optimization&nbsp\;can succeed even
  for a poor initial guess.
LOCATION:Seminar Room 1\, Newton Institute
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