Related papers: An inverse problem in estimating the time dependen…
By the recent advances in computer technology leading to the invention of more powerful processors, the importance of creating models using data training is even greater than ever. Given the significance of this issue, this work tries to…
We examine various density results related to the solutions of the non-local heat equation at a specific time slice, focusing on two distinct models: one with homogeneous Dirichlet boundary condition and the other with singular boundary…
This paper concerns the inverse source problem for the time-harmonic wave equation in a one dimensional domain. The goal is to determine the source function from the boundary measurements. The problem is challenging due to complexity of the…
Predicting the final hardness of steel after heat treatment is a challenging regression task due to the many-to-one nature of the process -- different combinations of input parameters (such as temperature, duration, and chemical…
This paper tackles the data completion problem related to the Helmholtz equation. The goal is to identify unknown boundary conditions on parts of the boundary that cannot be accessed directly, by making use of measurements collected from…
The aim of this paper is to establish the framework of the enclosure method for some class of inverse problems whose governing equations are given by parabolic equations with discontinuous coefficients. The framework is given by considering…
This work considers the inverse dynamic source problem arising from the time-domain fluorescence diffuse optical tomography (FDOT). We recover the dynamic distributions of fluorophores in biological tissue by the one single boundary…
In this work, ultrasonic guided waves and a dual-branch version of convolutional neural networks are used to solve two different but related inverse problems, i.e., finding layup sequence type and identifying material properties. In the…
We show the existence and optimal regularity of the optimal temperature configuration in a problem in heat conduction with minimal temperature constraint, interior heating and exterior insulation. Regularity of the two free boundaries is…
This paper addresses the set-point control problem of a heat equation with in-domain actuation. The proposed scheme is based on the framework of zero dynamics inverse combined with flat system control. Moreover, the set-point control is…
We investigate the inverse problem consisting in the identification of constant coefficients for a fractional-in-time partial differential equation governed by a finite sum of positive self-adjoint operators on a Hilbert space under…
An emerging line of work has shown that machine-learned predictions are useful to warm-start algorithms for discrete optimization problems, such as bipartite matching. Previous studies have shown time complexity bounds proportional to some…
Inverse optimization (Inverse optimal control) is the task of imputing a cost function such that given test points (trajectories) are (nearly) optimal with respect to the discovered cost. Prior methods in inverse optimization assume that…
This paper studies an inverse source problem for a viscoelastic membrane, where the material's memory effect is characterized by the Riemann-Liouville fractional derivative. The problem is to recover the unknown source term from the limited…
We prove logarithmic stability in the parabolic inverse problem of determining the space-varying factor in the source, by a single partial boundary measurement of the solution to the heat equation in an infinite closed waveguide, with…
The present article is dedicated to the forward and backward solution of a transient one-phase Stefan problem. In the forward problem, we compute the evolution of the initial domain for a Stefan problem where the melting temperature varies…
In this paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the unique continuation properties for elliptic and parabolic…
In this work the authors consider an inverse source problem in the following stochastic fractional diffusion equation $$\partial_t^\alpha u(x,t)+\mathcal{A} u(x,t)=f(x)h(t)+g(x) \dot{\mathbb{W}}(t).$$ The interested inverse problem is to…
We propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers. The approach is of Bayesian type, and it exploits a heavy-tailed t distribution for data noise…
We establish results for the injectivity and injectivity modulo gauge of certain inverse source problems in transport on a simply connected domain with variable index of refraction inducing a 'simple geometry'. The model given by radiative…