27th Conference of the International Linear Algebra Society (ILAS 2026)

Session

Model- and Data-driven Reduced-order Models and Their Applications in Inverse Problems

MS 34

May 18, 2026, 11:00 AM

345. Reduced order models for inverse scattering

Andreas Tataris

5/18/26, 11:00 AM

Model- and Data-driven Reduced-order Models and Their Applications in Inverse Problems

Minisymposium Talk

We present a numerical method for solving an inverse boundary value problem of estimating the acoustic velocity in the Helmholtz equation from frequency domain measurements based on reduced order models (ROM). The ROM is the Galerkin projection of the Helmholtz operator onto a subspace spanned by its solution snapshots at certain wavenumbers. We show how to reconstruct the ROM in a data-driven...

442. ROM-based Inverse Scattering for Monostatic Data

Jörn Zimmerling (Uppsala University)

5/18/26, 11:25 AM

Model- and Data-driven Reduced-order Models and Their Applications in Inverse Problems

Minisymposium Talk

We consider an inverse scattering problem for monostatic synthetic aperture radar (SAR), where the goal is to estimate the wave speed in a heterogeneous, isotropic medium using measurements from a moving antenna. The forward map, derived from Maxwell’s equations, is inherently nonlinear, accounts for multiple scattering, and exhibits high-frequency oscillations that make traditional nonlinear...

464. Multiparameter Waveform Inversion via Reduced Order Modeling

Alexander Mamonov (University of Houston)

5/21/26, 2:00 PM

Model- and Data-driven Reduced-order Models and Their Applications in Inverse Problems

Minisymposium Talk

Waveform inversion seeks to estimate an inaccessible heterogeneous medium from data gathered by sensors that emit probing signals and measure the generated waves. The traditional full waveform inversion (FWI) formulation estimates the unknown coefficients via minimization of the nonlinear, least squares data fitting objective function. For typical band-limited and high frequency data, this...

494. Characterization of the response of electric circuits with two kinds of passive elements

Fernando Guevara Vasquez (University of Utah)

5/21/26, 2:25 PM

Model- and Data-driven Reduced-order Models and Their Applications in Inverse Problems

Minisymposium Talk

The response matrix of an electrical circuits composed of two kinds of passive elements (e.g. LC, RC, CL...) is a matrix-valued rational function of the frequency that associates time-harmonic voltages at some terminal nodes to time-harmonic currents. We present necessary conditions that must be satisfied by the response matrix. These conditions can be used to construct circuits whose response...

502. Adaptive data-driven reduced-order models of port-Hamiltonian dynamical systems for nonlinear inverse scattering applications

Mikhail Zaslavskiy (Southern Methodist University)

5/21/26, 2:50 PM

Model- and Data-driven Reduced-order Models and Their Applications in Inverse Problems

Minisymposium Talk

The inverse scattering problem formulated for the Schrödinger operators arises in various fields, including quantum mechanics, radars, viscoelasticity, Biot problems, remote sensing, geophysical, and medical imaging. The goal of imaging is to find medium properties in the domain using near-field measured data. The model based nonlinear optimization which is the method of choice for the...