Related papers: Inverse Problems in PDF Determinations
Inverse problems are ubiquitous in the sciences and engineering. Two categories of inverse problems concerning a physical system are (1) estimate parameters in a model of the system from observed input-output pairs and (2) given a model of…
This article is devoted to the simultaneous resolution of three inverse problems, among the most important formulation of inverse problems for partial differential equations, stated for some class of diffusion equations from a single…
This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…
Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their…
In this paper, we propose and study several inverse problems of identifying/determining unknown coefficients for a class of coupled PDE systems by measuring the average flux data on part of the underlying boundary. In these coupled systems,…
We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…
We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data (quantities of interest). The solution, given as a probability measure, is…
We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field…
A complete solution for an inverse problem needs five main steps: choice of basis functions for discretization, determination of the order of the model, estimation of the hyperparameters, estimation of the solution, and finally,…
Inverse problems are prevalent in numerous scientific and engineering disciplines, where the objective is to determine unknown parameters within a physical system using indirect measurements or observations. The inherent challenge lies in…
Inverse problems are concerned with the reconstruction of unknown physical quantities using indirect measurements and are fundamental across diverse fields such as medical imaging, remote sensing, and material sciences. These problems serve…
A complete solution for an inverse problem needs five main steps: choice of basis functions for discretization, determination of the order of the model, estimation of the hyperparameters, estimation of the solution, and finally,…
Some calculations of parton distributions from first principles only give access to a limited range of Fourier modes of the function to reconstruct. We present a physically motivated procedure to regularize the inverse integral problem…
By suitable examples we illustrate an algorithm for composition of inverse problems.
The Bayesian approach has proved to be a coherent approach to handle ill posed Inverse problems. However, the Bayesian calculations need either an optimization or an integral calculation. The maximum a posteriori (MAP) estimation requires…
Robust Bayesian inference is the calculation of posterior probability bounds given perturbations in a probabilistic model. This paper focuses on perturbations that can be expressed locally in Bayesian networks through convex sets of…
In this paper we propose a new Bayesian estimation method to solve linear inverse problems in signal and image restoration and reconstruction problems which has the property to be scale invariant. In general, Bayesian estimators are {\em…
This paper is concerned with a Bayesian approach to testing hypotheses in statistical inverse problems. Based on the posterior distribution $\Pi \left(\cdot |Y = y\right)$, we want to infer whether a feature $\langle\varphi,…
A discussion is presented of the manner in which uncertainties in parton distributions and related quantities are determined. One of the central problems is the criteria used to judge what variation of the parameters describing a set of…
To quantify uncertainties in inverse problems of partial differential equations (PDEs), we formulate them into statistical inference problems using Bayes' formula. Recently, well-justified infinite-dimensional Bayesian analysis methods have…