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DTSTART:20070311T020000
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DTSTAMP:20240201T113228
DTSTART;TZID=America/Detroit:20240216T150000
DTEND;TZID=America/Detroit:20240216T160000
SUMMARY:Lecture / Discussion:AIM Seminar: Inverse wave scattering via data driven reduced order modeling
DESCRIPTION:Abstract: This talk is concerned with the following inverse problem for the wave equation: Determine the variable wave speed from data gathered by a collection of sensors\, which emit probing signals and measure the generated backscattered waves. Inverse backscattering is an interdisciplinary field driven by applications in geophysical exploration\, radar imaging\, non-destructive evaluation of materials\, etc. There are two types of methods:\n\n(1) Qualitative (imaging) methods\, which address the simpler problem of locating reflective\nstructures in a known host medium.\n\n(2) Quantitative methods\, also known as velocity estimation. Typically\, velocity estimation is\nformulated as a PDE constrained optimization\, where the data are fit in the least squares sense by\n\nthe wave computed at the search wave speed. The increase in computing power has lead to growing interest in this approach\, but there is a fundamental impediment\, which manifests especially for high frequency data: The objective function 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 approach to\nvelocity estimation\, based on a reduced order model (ROM) of the wave operator. The ROM is called\ndata driven because it is obtained from the measurements made at the sensors. The mapping between these measurements and the ROM is nonlinear\, and yet the ROM can be computed efficiently using methods from numerical linear algebra. More importantly\, the ROM can be used to define a better objective function for velocity estimation\, so that gradient based optimization can succeed even for a poor initial guess.\n\n(Joint work with Josselin Garnier\, Alexander Mamonov and John Zimmerling)\n\nContact: AIM Seminar Organizers
UID:114764-21833579@events.umich.edu
URL:https://events.umich.edu/event/114764
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1084
CONTACT:
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