Related papers: Inverse problems for linear parabolic equations us…
We consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. We analyze a lifting and decomposition approach into a mixed-integer optimal control problem without…
In this paper we consider the iteratively regularized Gauss-Newton method for solving nonlinear ill-posed inverse problems. Under merely Lipschitz condition, we prove that this method together with an a posteriori stopping rule defines an…
In this article, we dwell into the class of so-called ill-posed Linear Inverse Problems (LIP) which simply refers to the task of recovering the entire signal from its relatively few random linear measurements. Such problems arise in a…
In tomographic reconstruction, the goal is to reconstruct an unknown object from a collection of line integrals. Given a complete sampling of such line integrals for various angles and directions, explicit inverse formulas exist to…
We propose to solve inverse problems involving the temporal evolution of physics systems by leveraging recent advances from diffusion models. Our method moves the system's current state backward in time step by step by combining an…
In this paper we apply a scaling invariance analysis to reduce a class of parabolic moving boundary problems to free boundary problems governed by ordinary differential equations. As well known free boundary problems are always non-linear…
In this paper, we propose novel proper orthogonal decomposition (POD)--based model reduction methods that effectively address the issue of inverse crime in solving parabolic inverse problems. Both the inverse initial value problems and…
We study the application of the Augmented Lagrangian Method to the solution of linear ill-posed problems. Previously, linear convergence rates with respect to the Bregman distance have been derived under the classical assumption of a…
A new strategy based on numerical homogenization and Bayesian techniques for solving multiscale inverse problems is introduced. We consider a class of elliptic problems which vary at a microscopic scale, and we aim at recovering the highly…
We propose an approach based on quadratic approximations for solving general Mixed-Integer Nonlinear Programming (MINLP) problems. Specifically, our approach entails the global approximation of the epigraphs of constraint functions by means…
We consider the inverse problem of reconstructing the boundary curve of a cavity embedded in a bounded domain. The problem is formulated in two dimensions for the wave equation. We combine the Laguerre transform with the integral equation…
We propose in this paper a new numerical method to solve an inverse source problem for general hyperbolic equations. This is the problem of reconstructing sources from the lateral Cauchy data of the wave field on the boundary of a domain.…
The paper presents results about strong metric subregularity of the optimality mapping associated with the system of first-order necessary optimality conditions for a problem of optimal control of a semilinear parabolic equation. The…
The parareal in time algorithm allows to perform parallel simulations of time dependent problems. This algorithm has been implemented on many types of time dependent problems with some success. Recent contributions have allowed to extend…
We present a unified framework to construct well-posed formulations for large classes of linear operator equations including elliptic, parabolic and hyperbolic partial differential equations. This general approach incorporates known weak…
An inverse problem of finding an unknown heat source for a class of linear parabolic equations is considered. Such problems can typically be converted to a direct problem with non-local conditions in time instead of an initial value…
The Levenberg-Marquardt algorithm is one of the most popular algorithms for finding the solution of nonlinear least squares problems. Across different modified variations of the basic procedure, the algorithm enjoys global convergence, a…
Inverse problems in statistical physics are motivated by the challenges of `big data' in different fields, in particular high-throughput experiments in biology. In inverse problems, the usual procedure of statistical physics needs to be…
We study a degenerate parabolic-hyperbolic equation with zero flux boundary condition. The aim of this paper is to prove convergence of numerical approximate solutions towards the unique entropy solution. We propose an implicit finite…
In this work, we investigate the stability issue of the inverse problem of determining the locations and time-dependent amplitudes of point sources in a parabolic equation with a non-self adjoint elliptic operator from boundary…