[01168] Network based reduced-order models for forward and inverse PDE problems
Session Date & Time :
01168 (1/2) : 5B (Aug.25, 10:40-12:20)
01168 (2/2) : 5C (Aug.25, 13:20-15:00)
Type : Proposal of Minisymposium
Abstract : Reduced order models (ROMs) have been proven to be a powerful and versatile tool for a fast and robust large-scale simulations as well as imaging and inversion. In this minisymposium we will focus on a special class of ROMs, network-based ROMs, that originate from network synthesis. It allows to represent ROM in terms of sparsely-connected networks and enables a direct physical interpretation. We shall discuss various techniques to construct such ROMs as well as their applications.
Organizer(s) : Vladimir Druskin, Alexander Mamonov, Mikhail Zaslavskiy
[02869] Regularized Lippmann-Schwinger-Lanczos Algorithm for Inverse Scattering Problems in the Frequency Domain
Author(s) :
Justin Baker (University of Utah)
Elena Cherkaev (University of Utah)
Vladimir Druskin (Worcester Polytechnic Institute)
Shari Moskow (Drexel University)
Mikhail Zaslavsky (Schlumberger-Doll Research Center)
Abstract : Inverse scattering techniques have broad applicability in medical imaging, geophysics, and remote sensing. This talk presents a robust direct reduced order model (ROM) method for solving inverse scattering problems. The approach is based on a Lippmann-Schwinger-Lanczos (LSL)
algorithm in the frequency domain with two levels of regularization. Results of numerical experiments for Schrodinger and Helmholtz problems show that the proposed regularization scheme significantly improves the performance of the LSL algorithm, allowing for good reconstructions with noisy data.
[04751] Inverse scattering in attenuating media -- a ROM approach
Author(s) :
Jörn Zimmerling (Uppsala University)
Vladimir Druskin (WPI)
Rob Remis (TU Delft)
Abstract : Inverse scattering problems in attenuating media arise in important applications in biomedical imaging or radar imaging. In inverse scattering the goal is to reconstruct the coefficients of a PDE based on remote measurements of scattered waves. Based on these measurements a reduced-order model can be constructed that goes beyond the typical data fitting. It has a special algebraic structure that allows analogies to finite-difference discretization of PDEs and facilitates efficient solution of the inverse problem.
[04821] Can one identify damped Stieltjes string from its spectral function?
Author(s) :
Vladimir Druskin (WPI)
Jörn Zimmerling (Uppsala University)
Rob Remis (Delft University University)
Abstract : The Stieltjes strings were introduced by Gantmakher and Krein as isomorphic mechanical representations of the Stieltjes spectral functions. However, dissipative strings cannot be uniquely identified for the continuous spectral functions, corresponding to the unbounded domains. Generally, any passive transfer function can be represented as a Stieltjes function, that yields a wide class of equivalent solutions. We analyze constraints leading to the uniqueness for damped problems and numerical implementation in the data-driven ROM framework.
[05171] REDUCED ORDER MODELING INVERSION OF MONOSTATIC DATA IN A MULTI-SCATTERING ENVIRONMENT
Abstract : We consider the reduced order model approach for inversion in the monostatic formulation targeting the synthetic aperture radar (SAR) data in the time domain. The monostatic data is given as a series of single input/single output (SISO) responses due to moving collocated sources and receivers, that is, the diagonal of the matrix-valued MIMO transfer matrix. The ROMs are constructed to match the data for each source-receiver pair separately, and these are used to construct internal solutions for the corresponding source using only data-driven Gramian. The data from different locations is then coupled via the approximate Lippman-Schwinger integral equation. Numerical experiments illustrating the performance of our approach will be provided.
