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Inverse scattering has a broad applicability in quantum mechanics, remote sensing, geophysical, and medical imaging. This paper presents a robust direct reduced order model (ROM) method for solving inverse scattering problems based on an…

Numerical Analysis · Mathematics 2023-11-29 Justin Baker , Elena Cherkaev , Vladimir Druskin , Shari Moskow , Mikhail Zaslavsky

The objective of this work is to quantify the reconstruction error in sparse inverse problems with measures and stochastic noise, motivated by optimal sensor placement. To be useful in this context, the error quantities must be explicit in…

Numerical Analysis · Mathematics 2024-04-19 Phuoc-Truong Huynh , Konstantin Pieper , Daniel Walter

In this paper, we extend the ROM-based approach for inverse scattering with Neumann boundary conditions, introduced by Druskin at. al. (Inverse Problems 37, 2021), to the 1D Schr{\"o}dinger equation with impedance (Robin) boundary…

Numerical Analysis · Mathematics 2023-04-07 Tristan van Leeuwen , Andreas Tataris

In this paper, we study the inverse acoustic medium scattering problem to reconstruct the unknown inhomogeneous medium from far field patterns of scattered waves. We propose the reconstruction scheme based on the Kalman filter, which…

Analysis of PDEs · Mathematics 2021-10-19 Takashi Furuya , Roland Potthast

We propose an inverse-design approach for computational spectrometers in which the scattering media are topology-optimized to achieve better performance in inference of unknown spectra. Unlike traditional end-to-end approaches, our inverse…

Optics · Physics 2026-03-31 Wenchao Ma , Raphaël Pestourie , Zin Lin , Steven G. Johnson

This study focuses on the application of ultra sonic diffrac tion tomography to noncircular 2D-cylindri - cal ob jects im mersed in an in fi nite fluid. The dis torted Born it er a tive method used to solve the in verse scat ter ing prob…

Classical Physics · Physics 2009-12-17 Philippe Lasaygues , Régine Guillermin , Jean-Pierre Lefebvre

Self-organizing systems demonstrate how simple local rules can generate complex stochastic patterns. Many natural systems rely on such dynamics, making self-organization central to understanding natural complexity. A fundamental challenge…

Adaptation and Self-Organizing Systems · Physics 2026-01-12 Elias Najarro , Nicolas Bessone , Sebastian Risi

Numerical simulations of contaminant dispersion, as after a gas leakage incident on a chemical plant, can provide valuable insights for both emergency response and preparedness. Simulation approaches combine incompressible Navier-Stokes…

Computational Engineering, Finance, and Science · Computer Science 2026-03-05 Lisa Kühn , Jacopo Bonari , Max von Danwitz , Alexander Popp

For quantitative seismic imaging, iterative least-squares reverse time migration is the recommended approach. The existence of an inverse of the forward modelling operator would considerably reduce the number of required iterations. In the…

Geophysics · Physics 2020-12-11 Milad Farshad , Hervé Chauris

This work investigates projection-based Reduced-Order Models (ROMs) formulated in the frequency domain, employing a space-time basis constructed with Spectral Proper Orthogonal Decomposition to efficiently represent dominant spatio-temporal…

Fluid Dynamics · Physics 2026-01-12 Xiaodong Li , Davide Lasagna

This paper concerns the inverse source scattering problems of recovering random sources for acoustic and elastic waves. The underlying sources are assumed to be random functions driven by an additive white noise. The inversion process aims…

Numerical Analysis · Mathematics 2024-12-10 Yan Chang , Yukun Guo , Zhipeng Yang , Yue Zhao

A novel method for the numerical prediction of the slowly varying dynamics of nonlinear mechanical systems has been developed. The method is restricted to the regime of an isolated nonlinear mode and consists of a two-step procedure: In the…

Computational Engineering, Finance, and Science · Computer Science 2021-01-01 Malte Krack , Lars Panning-von Scheidt , Jörg Wallaschek

We consider an inverse acoustic scattering problem in simultaneously recovering an embedded obstacle and its surrounding inhomogeneous medium by formally determined far-field data. It is shown that the knowledge of the scattering amplitude…

Analysis of PDEs · Mathematics 2017-05-24 Hongyu Liu , Xiaodong Liu

Optical diffraction tomography relies on solving an inverse scattering problem governed by the wave equation. Classical reconstruction algorithms are based on linear approximations of the forward model (Born or Rytov), which limits their…

Computational Engineering, Finance, and Science · Computer Science 2017-09-01 Emmanuel Soubies , Thanh-An Pham , Michael Unser

We consider the inverse acoustic obstacle problem for sound-soft star-shaped obstacles in two dimensions wherein the boundary of the obstacle is determined from measurements of the scattered field at a collection of receivers outside the…

Numerical Analysis · Mathematics 2023-08-04 Mo Zhou , Jiequn Han , Manas Rachh , Carlos Borges

This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven…

Computational Engineering, Finance, and Science · Computer Science 2026-01-26 Alejandro N Diaz , Shane A McQuarrie , John T Tencer , Patrick J Blonigan

We consider the inverse scattering problem for time-harmonic acoustic waves in a medium with pointwise inhomogeneities. In the Foldy-Lax model, the estimation of the scatterers' locations and intensities from far field measurements can be…

Numerical Analysis · Mathematics 2024-07-25 Giovanni S. Alberti , Romain Petit , Matteo Santacesaria

Reduced Order Models (ROMs) form essential tools across engineering domains by virtue of their function as surrogates for computationally intensive digital twinning simulators. Although purely data-driven methods are available for ROM…

Computational Engineering, Finance, and Science · Computer Science 2025-04-14 Konstantinos Vlachas , Thomas Simpson , Anthony Garland , D. Dane Quinn , Charbel Farhat , Eleni Chatzi

Inferring unknown initial states in shock-dominated compressible flows from sparse and noisy measurements is a challenging ill-posed inverse problem due to nonlinear wave interactions and limited sensing. In this work, we develop a…

Machine Learning · Computer Science 2026-05-20 Bipin Tiwari , Muhammad Abid , Omer San

We present an algorithm for solving inverse problems on graphs analogous to those arising in diffuse optical tomography for continuous media. In particular, we formulate and analyze a discrete version of the inverse Born series, proving…

Combinatorics · Mathematics 2017-04-26 Francis J. Chung , Anna C. Gilbert , Jeremy G. Hoskins , John C. Schotland