Related papers: Stability and Concentration in Nonlinear Inverse P…
This paper develops a geometric framework for the stability analysis of differential inclusions governed by maximally monotone operators. A key structural decomposition expresses the operator as the sum of a convexified limit mapping and a…
The Lipschitz bound, a technique from robust statistics, can limit the maximum changes in the output concerning the input, taking into account associated irrelevant biased factors. It is an efficient and provable method for examining the…
This paper establishes comprehensive stability results for quasi-variational inequalities (QVIs) under monotone perturbations of the governing operator. We prove strong convergence of both minimal and maximal solutions when sequences of…
In this paper, we consider the inverse problem of recovering a diffusion and absorption coefficients in steady-state optical tomography problem from the Neumann-to-Dirichlet map. We first prove a Global uniqueness and Lipschitz stability…
Inverse nodal problem on diffusion operator is the problem of finding the potential functions and parameters in the boundary conditions by using nodal data. In particular, we solve the reconstruction and stability problems using nodal set…
In this paper we study the inverse boundary value problem of determining the potential in the Schr\"{o}dinger equation from the knowledge of the Dirichlet-to-Neumann map, which is commonly accepted as an ill-posed problem in the sense that,…
We consider the problem of recovering a real-valued $n$-dimensional signal from $m$ phaseless, linear measurements and analyze the amplitude-based non-smooth least squares objective. We establish local convergence of subgradient descent…
We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequency as the data. We develop an explicit reconstruction of the wavespeed using a multi-level nonlinear projected…
We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequencies as the data. A conditional Lipschitz stability estimate for the inverse problem holds in the case of…
In this paper, we consider the inverse problem of detecting a corrosion coefficient between two layers of a conducting medium from the Neumann-to-Dirichlet map. This inverse problem is motivated by the description of the index of corrosion…
Numerous state-feedback and observer designs for nonlinear dynamic systems (NDS) have been developed in the past three decades. These designs assume that NDS nonlinearities satisfy one of the following function set classifications: bounded…
We consider a neural network architecture designed to solve inverse problems where the degradation operator is linear and known. This architecture is constructed by unrolling a forward-backward algorithm derived from the minimization of an…
We develop a finite-dimensional sensitivity framework for studying stability in learning systems whose states include representations, parameters, and update variables. The central object is the \emph{Learning Stability Profile}, a…
The primary objective of this research is to investigate an inverse problem of parameter identification in nonlinear mixed quasi-variational inequalities posed in a Banach space setting. By using a fixed point theorem, we explore properties…
A generalized dynamical robust nonlinear filtering framework is established for a class of Lipschitz differential algebraic systems, in which the nonlinearities appear both in the state and measured output equations. The system is assumed…
In this article, we provide stability estimates for the finite element discretization of a class of inverse parameter problems of the form $-\nabla\cdot(\mu S) = \g f$ in a domain $\Omega$ of $\R^d$. Here $\mu$ is the unknown parameter to…
Using uniform global Carleman estimates for discrete elliptic and semi-discrete hyperbolic equations, we study Lipschitz and logarithmic stability for the inverse problem of recovering a potential in a semi-discrete wave equation,…
A review of the author's results is given. Inversion formulas and stability estimates for the solutions to 3D inverse scattering problems with fixed-energy data are obtained. Inversions of exact and noisy data are stidied. The inverse…
Inverse transport theory concerns the reconstruction of the absorption and scattering coefficients in a transport equation from knowledge of the albedo operator, which models all possible boundary measurements. Uniqueness and stability…
This work establishes rigorous, novel and widely applicable stability guarantees and transferability bounds for graph convolutional networks -- without reference to any underlying limit object or statistical distribution. Crucially,…