English
Related papers

Related papers: Time reversal methods in unknown medium and invers…

200 papers

We propose a time-domain boundary integral method to model linear wave propagation with refractive, focusing, and Doppler effects arising from medium heterogeneities and moving obstacles. In contrast to existing techniques, our method…

Numerical Analysis · Mathematics 2026-05-13 Raaghav Ramani

The time reversal method in thermoacoustic tomography is used for approximating the initial pressure inside a biological object using measurements of the pressure wave made on a surface surrounding the object. This article presents error…

Analysis of PDEs · Mathematics 2009-03-18 Yulia Hristova

The recently developed globally convergent numerical method for an inverse medium problem for the Helmholtz equation is tested on experimental data. The data were originally collected in the time domain, whereas the method works in the…

Numerical Analysis · Mathematics 2016-10-26 Aleksandr E. Kolesov , Michael V. Klibanov , Loc H. Nguyen , Dinh-Liem Nguyen , Nguyen T. Thanh

We present an end-to-end framework for generating solutions to combinatorial optimization problems with unknown components using transformer-based sequence-to-sequence neural networks. Our framework learns directly from past solutions and…

Optimization and Control · Mathematics 2026-02-06 Macarena Navarro , Willem-Jan van Hoeve , Karan Singh

The utilization of time reversal symmetry in designing and implementing (quantum) optical experiments has become more and more frequent over the past years. We review the basic idea underlying time reversal methods, illustrate it with…

Optics · Physics 2012-05-08 Gerd Leuchs , Markus Sondermann

We present an efficient, effective, and generic approach towards solving inverse problems. The key idea is to leverage the feedback signal provided by the forward process and learn an iterative update model. Specifically, at each iteration,…

Computer Vision and Pattern Recognition · Computer Science 2021-01-20 Wei-Chiu Ma , Shenlong Wang , Jiayuan Gu , Sivabalan Manivasagam , Antonio Torralba , Raquel Urtasun

In a Bayesian setting, inverse problems and uncertainty quantification (UQ) --- the propagation of uncertainty through a computational (forward) model --- are strongly connected. In the form of conditional expectation the Bayesian update…

This paper develops a discrete data-driven approach for solving the inverse source problem of the wave equation with final time measurements. Focusing on the $L^2$-Tikhonov regularization method, we analyze its convergence under two…

Numerical Analysis · Mathematics 2026-01-01 Qiling Gu , Wenlong Zhang , Zhidong Zhang

This paper concerns an inverse elastic scattering problem which is to determine a rigid obstacle from time domain scattered field data for a single incident plane wave. By using Helmholtz decomposition, we reduce the initial-boundary value…

Numerical Analysis · Mathematics 2022-03-14 Lu Zhao , Heping Dong , Fuming Ma

A new method is proposed to improve the numeri- cal simulation of time dependent problems when the initial and boundary data are not compatible. Unlike earlier methods limited to space dimension one, this method can be used for any space…

Numerical Analysis · Mathematics 2010-11-23 Qingshan Chen , Zhen Qin , Roger Temam

This article addresses the inverse problem of simultaneously recovering both the wave speed coefficient and an unknown initial condition (acting as the source) for the multidimensional wave equation from a single passive boundary…

Analysis of PDEs · Mathematics 2025-07-29 Yavar Kian , Hongyu Liu

This paper is devoted to a novel quantitative imaging scheme of identifying impenetrable obstacles in time-harmonic acoustic scattering from the associated far-field data. The proposed method consists of two phases. In the first phase, we…

Numerical Analysis · Mathematics 2023-07-05 Youzi He , Hongyu Liu , Xianchao Wang

Numerical solutions to Newton's equations of motion for chaotic self gravitating systems of more than 2 bodies are often regarded to be irreversible. This is due to the exponential growth of errors introduced by the integration scheme and…

Instrumentation and Methods for Astrophysics · Physics 2018-03-14 Simon Portegies Zwart , Tjarda Boekholt

Model predictive control solves a constrained optimization problem online in order to compute an implicit closed-loop control policy. Recursive feasibility -- guaranteeing that the optimal control problem will have a solution at every time…

Optimization and Control · Mathematics 2024-10-16 Jacob W. Knaup , Panagiotis Tsiotras

Inverse wave scattering aims at determining the properties of an object using data on how the object scatters incoming waves. In order to collect information, sensors are put in different locations to send and receive waves from each other.…

Machine Learning · Computer Science 2026-01-22 Hanyang Jiang , Yuehaw Khoo , Haizhao Yang

The paper surveys recent progress in establishing uniqueness and developing inversion formulas and algorithms for the thermoacoustic tomography. In mathematical terms, one deals with a rather special inverse problem for the wave equation.…

Analysis of PDEs · Mathematics 2009-02-02 M. Agranovsky , P. Kuchment , L. Kunyansky

We study an inverse problem for the wave equation where localized wave sources in random scattering media are to be determined from time resolved measurements of the waves at an array of receivers. The sources are far from the array, so the…

Mathematical Physics · Physics 2016-07-18 Liliana Borcea , Ilker Kocyigit

We study the inverse problem of determining both the source of a wave and its speed inside a medium from measurements of the solution of the wave equation on the boundary. This problem arises in photoacoustic and thermoacoustic tomography,…

Analysis of PDEs · Mathematics 2019-06-18 Christina Knox , Amir Moradifam

We consider the inverse problem of recovering both an unknown electric current and the surrounding electromagnetic parameters of a medium from boundary measurements. This inverse problem arises in brain imaging. We show that under generic…

Analysis of PDEs · Mathematics 2017-10-25 Youjun Deng , Hongyu Liu , Gunther Uhlmann

We consider the inverse dynamic problem for the wave equation with a potential on an interval $(0,2\pi)$ with periodic boundary conditions. We use a boundary triplet to set up the initial-boundary value problem. As an inverse data we use a…

Analysis of PDEs · Mathematics 2025-05-27 A. S. Mikhaylov , V. S. Mikhaylov