Related papers: Inverse problems for semiconductors: models and me…
A general shape identification inverse problem is studied in a Bayesian framework. This problem requires the determination of the unknown shape of a domain in the Euclidean space from finite-dimensional observation data with some Gaussian…
We study the inverse eigenvector centrality problem on connected undirected graphs, namely, whether a given positive vector can be realized by assigning suitable edge weights. We provide a complete characterization in terms of stable sets…
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…
The level set method is a widely used tool for solving reachability and invariance problems. However, some shortcomings, such as the difficulties of handling dissipation function and constructing terminal conditions for solving the…
In this paper we consider new regularization methods for linear inverse problems of dynamic type. These methods are based on dynamic programming techniques for linear quadratic optimal control problems. Two different approaches are…
In this article, we develop and present a novel regularization scheme for ill-posed inverse problems governed by nonlinear time-dependent partial differential equations (PDEs). In our recent work, we introduced a bi-level regularization…
Metasurfaces with bound states in the continuum (BICs) have proven to be a powerful platform for drastically enhancing light-matter interactions, improving biosensing, and precisely manipulating near- and far-fields. However, engineering…
We consider inverse boundary value problems for general real principal type differential operators. The first results state that the Cauchy data set uniquely determines the scattering relation of the operator and bicharacteristic ray…
We consider Sturm-Liouville problems with a discontinuity in an interior point, which are motivated by the inverse problems for the torsional modes of the Earth. We assume that the potential on the right half-interval and the coefficient in…
In many physical systems, inputs related by intrinsic system symmetries are mapped to the same output. When inverting such systems, i.e., solving the associated inverse problems, there is no unique solution. This causes fundamental…
Using existing, forward-in-time integration schemes, we demonstrate that it is possible to compute unstable, saddle-type fixed points of stiff systems of ODEs when the stable compenents are fast (i.e., rapidly damped) while the unstable…
In the present paper, we consider a non self adjoint hyperbolic operator with a vector field and an electric potential that depend not only on the space variable but also on the time variable. More precisely, we attempt to stably and…
Plug-and-play diffusion priors (PnPDP) have emerged as a promising research direction for solving inverse problems. However, current studies primarily focus on natural image restoration, leaving the performance of these algorithms in…
We are interested in an inverse medium problem with internal data. This problem is originated from multi-waves imaging. We aim in the present work to study the well-posedness of the inversion in terms of the boundary conditions. We…
We consider the statistical inverse problem of estimating a background flow field (e.g., of air or water) from the partial and noisy observation of a passive scalar (e.g., the concentration of a solute), a common experimental approach to…
Sum of a second derivative operator with periodic boundary conditions and an integral operator of rank one (non-local potential) is studied in this manuscript. Not only spectral analysis is conducted for this operator but the inverse…
In this paper, we study inverse boundary problems associated with semilinear parabolic systems in several scenarios where both the nonlinearities and the initial data can be unknown. We establish several simultaneous recovery results…
Solving inverse partial differential equation (PDE) problems is a fundamental topic in scientific research due to its broad significance across a wide range of real-world applications. Inverse PDE problems arise across medical imaging,…
We consider the self-adjoint Dirac operators on a finite interval with summable matrix-valued potentials and general boundary conditions. For such operators, we study the inverse problem of reconstructing the potential and the boundary…
Determining kinetic rate constants is a highly relevant problem in biochemistry, so various methods have been designed to extract them from experimental data. Such methods have two main components: the experimental apparatus and the…