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
Format : Talk at Waseda University
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.
[04821] Can one identify damped Stieltjes string from its spectral function?
Format : Talk at Waseda University
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.
[04751] Inverse scattering in attenuating media -- a ROM approach
Format : Talk at Waseda University
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.
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.
[05531] Waveform Inversion via Reduced Order Modeling
Format : Talk at Waseda University
Author(s) :
Alexander Mamonov (University of Houston)
Liliana Borcea (University of Michigan)
Josselin Garnier (Ecole Polytechnique)
Jorn Zimmerling (Uppsala University)
Abstract : We propose a novel approach to full waveform inversion (FWI), based on a data driven reduced order model (ROM) of the wave equation operator. The unknown medium is probed with pulses and the time domain pressure waveform data is recorded on an active array of sensors. The ROM is a projection of the wave equation operator on a subspace of wave equation solution snapshots. It can be constructed from the measured data via a nonlinear process and subsequently used for efficient velocity estimation. While the conventional FWI via nonlinear least-squares data fitting is challenging without low frequency information, and prone to getting stuck in local minima (cycle skipping effect), minimization of ROM misfit is behaved much better, even for a poor initial guess. For low-dimensional parametrizations of the unknown velocity the ROM misfit function is demonstrably close to convex. The proposed approach consistently outperforms conventional FWI in standard synthetic tests, as shown in the numerical experiments.
[05544] Correlation-informed dictionary learning for imaging in complex media
Format : Talk at Waseda University
Author(s) :
Alexei Novikov (Penn State University)
Abstract : We propose an approach for imaging in strongly scattering media that uses dictionary learning and connectivity information to estimate the sensing matrices in these media. It has two steps. The first step estimates, with high accuracy, the true Green’s function vectors using array data from multiple sparse sets of sources, whose locations and amplitudes are not known to us. This step yields a dictionary for wave propagation whose columns are those of the sensing matrix up to permutations. The second step orders these columns using Multi-Dimensional Scaling (MDS) with connectivity information derived from cross-correlations of the estimated Green’s function vectors. For these two steps to work together, we must combine data from large and small arrays. Through simulation experiments, we show that the proposed approach is robust and is able to provide high-resolution images.
