Data driven reduced order models for inverse problems in heterogeneous media
Abstract
The goal of this collaborative proposal is to develop from first principles a novel methodology forinverse problems in heterogeneous media. The research borrows some ideas from reduced ordermodeling and machine learning, but it is targeted toward solving inverse problems for hyperbolicand parabolic partial differential equations (PDEs) that arise in applications relevant to the Navymission: coherent imaging with waves in random media, sea mine localization, and estimation ofthickness of sea ice. The sought inversion methodology has the following attributes: (1) It is datadriven, meaning that it operates without prior knowledge of the medium modeled by unknowncoefficients in the PDE. (2) It works with data that are generic in inverse problems, correspondingto time resolved measurements of the solution of the PDE at a few remote sensor locations. (3) It isdeeply rooted in the physics of the problem. (4) It offers an advantage over the existing inversionmethodology in terms of convergence of the algorithm and quality of the reconstructions of theunknown coefficients.The proposed research is organized in three distinct themes that are motivated by differentapplications:The first theme is concerned with coherent imaging in random media, from measurements ofthe wave field collected by an active array of sensors. It constructs a data driven reduced ordermodel (ROM) of the wave propagator operator which models the evolution of the wave in theunknown medium. The ROM is a matrix that describes this evolution in a Galerkin approximationspace. The challenge addressed in the proposal is how to use it for improving the existing coherentimaging methodology in random media.The second research theme is motivated by the application of imaging sea mines. It considers:(1) A ROM approach for imaging with low frequency electromagnetic waves in a conductivemedium, like sea water, which can be used for locating bottom and buried mines. (2) A ROMsonar array imaging approach that can mitigate multiple scattering effects from interfaces like thesea surface and the ocean floor, and can be used for locating moored mines in shallow water.The third research theme pursues a ROM based synthetic aperture radar imaging methodologyfor layered or nearly layered lossy media. It is motivated in part by the application of estimatingthe thickness of sea ice with low frequency electromagnetic waves.1Approved for Public Release
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- May 05, 2021
- Source ID
- N000142112370
Entities
People
- Liliana Borcea
Organizations
- Board of Regents of the University of Michigan
- Office of Naval Research
- United States Navy