Related papers: Model selection for inverse problems: Best choice …
We study the inverse problem of recovering the order and the diffusion coefficient of an elliptic fractional partial differential equation from a finite number of noisy observations of the solution. We work in a Bayesian framework and show…
A class of algorithms for the solution of discrete material optimization problems in electromagnetic applications is discussed. The idea behind the algorithm is similar to that of the sequential programming. However, in each major iteration…
We study an inverse scattering problem for a generic hyperbolic system of equations with an unknown coefficient called the reflectivity. The solution of the system models waves (sound, electromagnetic or elastic), and the reflectivity…
In this paper we consider ill-posed inverse problems, both linear and nonlinear, by a heavy ball method in which a strongly convex regularization function is incorporated to detect the feature of the sought solution. We develop ideas on how…
Computer models, aiming at simulating a complex real system, are often calibrated in the light of data to improve performance. Standard calibration methods assume that the optimal values of calibration parameters are invariant to the model…
Conventional inverse optimization inputs a solution and finds the parameters of an optimization model that render a given solution optimal. The literature mostly focuses on inferring the objective function in linear problems when accepted…
This paper introduces a novel deep neural network architecture for solving the inverse scattering problem in frequency domain with wide-band data, by directly approximating the inverse map, thus avoiding the expensive optimization loop of…
Obtaining meaningful solutions for inverse problems has been a major challenge with many applications in science and engineering. Recent machine learning techniques based on proximal and diffusion-based methods have shown promising results.…
Formulating a statistical inverse problem as one of inference in a Bayesian model has great appeal, notably for what this brings in terms of coherence, the interpretability of regularisation penalties, the integration of all uncertainties,…
The problem of pattern selection arises when the evolution equations have many solutions, whereas observed patterns constitute a much more restricted set. An approach is advanced for treating the problem of pattern selection by defining the…
The simulation of electric rotating machines is both computationally expensive and memory intensive. To overcome these costs, model order reduction techniques can be applied. The focus of this contribution is especially on machines that…
A new parameter choice rule for inverse problems is introduced. This parameter choice rule was developed for total variation regularization in electron tomography and might in general be useful for $L^1$ regularization of inverse problems…
The determination of Parton Distribution Functions from a finite set of data is a typical example of an inverse problem. Inverse problems are notoriously difficult to solve, in particular when a robust determination of the uncertainty in…
We consider the problem of reconstructing the shape of an impenetrable sound-soft obstacle from scattering measurements. The input data is assumed to be the far-field pattern generated when a plane wave impinges on an unknown obstacle from…
Inverse problems arise anywhere we have indirect measurement. As, in general they are ill-posed, to obtain satisfactory solutions for them needs prior knowledge. Classically, different regularization methods and Bayesian inference based…
We consider the inverse elastic scattering problems using the far field data due to one incident plane wave. A simple method is proposed to reconstruct the location and size of the obstacle using different components of the far field…
Clusters of wave-scattering oscillators offer the ability to passively control wave energy in elastic continua. However, designing such clusters to achieve a desired wave energy pattern is a highly nontrivial task. While the forward…
Invariant coordinate selection is an unsupervised multivariate data transformation useful in many contexts such as outlier detection or clustering. It is based on the simultaneous diagonalization of two affine equivariant and positive…
This paper is devoted to the algorithmic development of inverse elastic scattering problems. We focus on reconstructing the locations and shapes of elastic scatterers with known dictionary data for the nearly incompressible materials. The…
The tractions that cells exert on a gel substrate from the observed displacements is an increasingly attractive and valuable information in biomedical experiments. The computation of these tractions requires in general the solution of an…