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We look at continuum solutions in optimisation problems associated to linear inverse problems $y = Ax$ with non-negativity constraint $x \geq 0$. We focus on the case where the noise model leads to maximum likelihood estimation through…

Optimization and Control · Mathematics 2023-04-20 Camille Pouchol , Olivier Verdier

Consider an inverse problem of the simultaneous recovery of boundary impedance and internal conductivity in the electrical impedance tomography (EIT) model using local internal measurement data, which is governed by a boundary value problem…

Analysis of PDEs · Mathematics 2025-09-22 Jinchao Pan , Jijun Liu

This work concerns inverse boundary value problems for the time-harmonic Maxwell's equations on differential $1-$forms. We formulate the boundary value problem on a $3-$dimensional compact and simply connected Riemannian manifold $M$ with…

Analysis of PDEs · Mathematics 2023-03-14 Sean Holman , Vasiliki Torega

The minimal supersymmetric extension of the standard model allows for some of the coupling strengths to be complex parameters. The presence of such imaginary phases can lead to violations of time reversal invariance, which can be tested if…

High Energy Physics - Phenomenology · Physics 2009-10-22 E. Christova , M. Fabbrichesi

The need to blend observational data and mathematical models arises in many applications and leads naturally to inverse problems. Parameters appearing in the model, such as constitutive tensors, initial conditions, boundary conditions, and…

Statistics Theory · Mathematics 2010-09-16 J. Nolen , G. A. Pavliotis , A. M. Stuart

We propose a method to reconstruct the electrical current density from acoustically-modulated boundary measurements of time-harmonic electromagnetic fields. We show that the current can be uniquely reconstructed with Lipschitz stability. We…

Analysis of PDEs · Mathematics 2022-02-25 Wei Li , John C. Schotland , Yang Yang , Yimin Zhong

The polarization tomography problem consists of recovering a matrix function f from the fundamental matrix of the equation $D\eta/dt=\pi_{\dot\gamma}f\eta$ known for every geodesic $\gamma$ of a given Riemannian metric. Here…

Mathematical Physics · Physics 2009-11-13 Roman Novikov , Vladimir Sharafutdinov

This paper deals with the numerical approximation of the biharmonic inverse source problem in an abstract setting in which the measurement data is finite-dimensional. This unified framework in particular covers the conforming and…

Numerical Analysis · Mathematics 2021-06-15 Devika Shylaja , M. T. Nair

This paper proposes a new mathematical formulation for flow measurement based on the inverse source problem for wave equations with partial boundary measurement. Inspired by the design of acoustic Doppler current profilers (ADCPs), we…

Optimization and Control · Mathematics 2025-03-19 Jiwei Li , Lingyun Qiu , Zhongjing Wang , Hui Yu

Regularization is a critical technique for ensuring well-posedness in solving inverse problems with incomplete measurement data. Traditionally, the regularization term is designed based on prior knowledge of the unknown signal's…

Numerical Analysis · Mathematics 2024-12-16 Bosu Choi , Jihun Han , Yoonsang Lee

We study an inverse problem that consists in estimating the first (zero-order) moment of some R2-valued distribution m supported within a closed interval S $\subset$ R, from partial knowledge of the solution to the Poisson-Laplace partial…

Functional Analysis · Mathematics 2019-03-28 Juliette Leblond , Elodie Pozzi

We consider inverse problems related to the velocity reconstruction in electrically conducting fluids from externally measured magnetic fields. The underlying theory is presented in the framework of the integral equation approach to…

Fluid Dynamics · Physics 2007-05-23 Frank Stefani , Thomas Gundrum , Gunter Gerbeth , Uwe Guenther , Mingtian Xu

This paper is concerned with an inverse moving point source problem in electromagnetics. The aim is to reconstruct the moving orbit from the tangential components of magnetic fields taken at a finite number of observation points. The…

Numerical Analysis · Mathematics 2025-07-22 Minghui Li , Guanghui Hu , Yue Zhao

In this work, we investigate the regularized solutions and their finite element solutions to the inverse source problems governed by partial differential equations, and establish the stochastic convergence and optimal finite element…

Numerical Analysis · Mathematics 2021-10-25 Zhiming Chen , Wenlong Zhang , Jun Zou

Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…

Optimization and Control · Mathematics 2017-12-27 Anil Aswani , Zuo-Jun Max Shen , Auyon Siddiq

In this paper we consider the solution of monotone inverse problems using the particular example of a parameter identification problem for a semilinear parabolic PDE. For the regularized solution of this problem, we introduce a total…

Numerical Analysis · Mathematics 2025-02-26 Pankaj Gautam , Markus Grasmair

This article studies the inverse problem of recovering a nonlinearity in an elliptic equation $\Delta u + a(x,u) = 0$ from boundary measurements of solutions. Previous results based on first order linearization achieve this under a sign…

Analysis of PDEs · Mathematics 2026-05-08 David Johansson , Janne Nurminen , Mikko Salo

Differential regularization is applied to a field theory of a non-relativistic charged boson field $\phi$ with $\lambda (\phi {}^{*} \phi)^2$ self-interaction and coupling to a statistics-changing $U(1)$ Chern-Simons gauge field.…

High Energy Physics - Theory · Physics 2009-10-08 D. Z. Freedman , G. Lozano , N. Rius

We consider an inverse boundary value problem for a model time-harmonic equation of acoustic tomography of moving fluid with variable current velocity, sound speed, density and absorption. In the present article it is assumed that at fixed…

Analysis of PDEs · Mathematics 2017-02-14 Alexey Agaltsov

In this paper, we develop a framework for the discretization of a mixed formulation of quasi-reversibility solutions to ill-posed problems with respect to Poisson's equations. By carefully choosing test and trial spaces a formulation that…

Numerical Analysis · Mathematics 2024-10-01 Erik Burman , Mingfei Lu