Related papers: Inverse Problems in PDF Determinations
This paper studies a fundamental mechanism of how to detect a conflict between arguments given sentiments regarding acceptability of the arguments. We introduce a concept of the inverse problem of the abstract argumentation to tackle the…
We present a computational framework for estimating the uncertainty in the numerical solution of linearized infinite-dimensional statistical inverse problems. We adopt the Bayesian inference formulation: given observational data and their…
A variety of approaches has been developed to deal with uncertain optimization problems. Often, they start with a given set of uncertainties and then try to minimize the influence of these uncertainties. Depending on the approach used, the…
In robust optimization, the general aim is to find a solution that performs well over a set of possible parameter outcomes, the so-called uncertainty set. In this paper, we assume that the uncertainty size is not fixed, and instead aim at…
We investigate the convergence rates of variational posterior distributions for statistical inverse problems involving nonlinear partial differential equations (PDEs). Departing from exact Bayesian inference, variational inference…
Under consideration are mathematical models of heat and mass transfer. We study inverse problems of recovering lower-order coefficients in a second order parabolic equation. The coefficients are representable in the form of a finite…
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…
Bayesian approach, as a useful tool for quantifying uncertainties, has been widely used for solving inverse problems of partial differential equations (PDEs). One of the key difficulties for employing Bayesian approach for the issue is how…
In this work, we investigate the use of Besov priors in the context of Bayesian inverse problems. The solution to Bayesian inverse problems is the posterior distribution which naturally enables us to interpret the uncertainties. Besov…
In this paper we investigate the Bayesian approach to inverse Robin problems. These are problems for certain elliptic boundary value problems of determining a Robin coefficient on a hidden part of the boundary from Cauchy data on the…
We survey some of our recent results on inverse problems for evolution equations. The goal is to provide a unified approach to solve various types of evolution equations. The inverse problems we consider consist in determining unknown…
The present paper proposes a Bayesian framework for inverse problems that seamlessly integrates optimization and inversion to enable rapid surrogate modeling, accurate parameter inference, and rigorous uncertainty quantification. Bayesian…
We consider the generic problem of performing a global fit to many independent data sets each with a different overall multiplicative normalization uncertainty. We show that the methods in common use to treat multiplicative uncertainties…
In this chapter, we mainly review theoretical results on inverse source problems for diffusion equations with the Caputo time-fractional derivatives of order $\alpha\in(0,1)$. Our survey covers the following types of inverse problems: 1.…
This paper is concerned with the inverse moving source problems for parabolic equations. Given the temporal function, we prove the uniqueness of the nonlinear inverse problem of determining the orbit function by final data measured in a…
A thorough understanding of the issues surrounding the determination of parton distributions is crucial due to their importance to calculations of LHC observables. However, it is still not fully understood how much of an impact…
Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…
We consider Calderon's inverse problem with partial data in dimensions $n \geq 3$. If the inaccessible part of the boundary satisfies a (conformal) flatness condition in one direction, we show that this problem reduces to the invertibility…
The problem of the determination of the charge density from limited information about the charge form factor is an ill-posed inverse problem. A Bayesian probabilistic approach to this problem which permits to take into account both errors…
We consider optimal design of infinite-dimensional Bayesian linear inverse problems governed by partial differential equations that contain secondary reducible model uncertainties, in addition to the uncertainty in the inversion parameters.…