相关论文: Inverse coefficient problem for cascade system of …
The present manuscript consists of inverse problems for a coupled system of wave equations with potential in $\mathbb{R}^3$. By establishing the fundamental solution to the aforementioned operator, we study the uniqueness aspects of the…
This paper is devoted to the problem of sampling Gaussian fields in high dimension. Solutions exist for two specific structures of inverse covariance : sparse and circulant. The proposed approach is valid in a more general case and…
This paper is concerned with the inverse scattering problem which aims to determine the spatially distributed dielectric constant coefficient of the 2D Helmholtz equation from multifrequency backscatter data associated with a single…
This book aims to provide a brief overview of recent advancements in the theory of inverse problems for stochastic partial differential equations. In order to keep the content concise, we will only discuss the inverse problems of two…
In this paper, we consider the direct and inverse problem for isotropic scatterers with two conductive boundary conditions. First, we show the uniqueness for recovering the coefficients from the known far-field data at a fixed incident…
A new numerical method to solve an inverse source problem for the radiative transfer equation involving the absorption and scattering terms, with incomplete data, is proposed. No restrictive assumption on those absorption and scattering…
An inverse problem for the wave equation outside an obstacle with a {\it dissipative boundary condition} is considered. The observed data are given by a single solution of the wave equation generated by an initial data supported on an open…
This paper is concerned with the inverse problem of determining an obstacle and the corresponding incident point sources in the Helmholtz equation from near-field scattering data. An optimization method is proposed to simultaneously recover…
The inverse problem method is tested for a class of mean field statistical mechanics models representing a mixture of particles of different species. The robustness of the inversion is investigated for different values of the physical…
An inverse problem of the determination of an initial condition in a hyperbolic equation from the lateral Cauchy data is considered. This problem has applications to the thermoacoustic tomography, as well as to linearized coefficient…
We propose a double obstacle phase field approach to the recovery of piece-wise constant diffusion coefficients for elliptic partial differential equations. The approach to this inverse problem is that of optimal control in which we have a…
In this paper, we present an inverse problem of identifying the reaction coefficient for time fractional diffusion equations in two dimensional spaces by using boundary Neumann data. It is proved that the forward operator is continuous with…
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…
A novel numerical method for solving inverse scattering problem with fixed-energy data is proposed. The method contains a new important concept: the stability index of the inversion problem. This is a number, computed from the data, which…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
In this work, we study the inverse problem of recovering a potential coefficient in the subdiffusion model, which involves a Djrbashian-Caputo derivative of order $\alpha\in(0,1)$ in time, from the terminal data. We prove that the inverse…
This paper explores the reconstruction of a space-dependent parameter in inverse diffusion problems, proposing a shape-optimization-based approach. We consider a Robin boundary condition, physically motivated in diffuse optical tomography…
Coupled oscillators are prevalent throughout the physical world. Dynamical system formulations of weakly coupled oscillator systems have proven effective at capturing the properties of real-world systems. However, these formulations usually…
The inverse problem method is tested for a class of monomer-dimer statistical mechanics models that contain also an attractive potential and display a mean-field critical point at a boundary of a coexistence line. The inversion is obtained…
In this paper we solve the inverse problem for a class of mean field models (Curie-Weiss model and its multi-species version) when multiple thermodynamic states are present, as in the low temperature phase where the phase space is…