A MEASURE-THEORETIC COMPUTATIONAL METHOD FOR INVERSE SENSITIVITY PROBLEMS I: METHOD AND ANALYSIS

We consider the inverse sensitivity analysis problem of quantifying the uncertainty of inputs to a deterministic map given specified uncertainty in a linear functional of the output of the map. This is a version of the model calibration or parameter estimation problem for a deterministic map. We ass...

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Bibliographic Details
Published in:SIAM journal on numerical analysis Vol. 49; no. 5/6; pp. 1836 - 1859
Main Authors: BREIDT, J., BUTLER, T., ESTEP, D.
Format: Journal Article
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.09.2011
Subjects:
Adjoints
Aeronautics
Alloys
Approximation
Density
Determinism
Exact sciences and technology
Global analysis, analysis on manifolds
Heat
Inverse problems
Laboratories
Load
Mathematical analysis
Mathematical independent variables
Mathematics
Numerical analysis
Numerical analysis in abstract spaces
Numerical analysis. Scientific computation
Numerical linear algebra
Parameter estimation
Parametric models
Random variables
Real functions
Sciences and techniques of general use
Sensitivity analysis
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Values
nonparametric density estimation
Parameter estimation
Sensitivity analysis
Approximation
Numerical linear algebra
model calibration
Probability distribution
34F05
Inverse problem
Regularization method
inverse sensitivity analysis
Numerical analysis
60-08
set-valued inverse
Distribution function
adjoint problem
Ill posed problem
Linear functional
Random variable
density estimation
sensitivity analysis
parameter estimation
ISSN:0036-1429, 1095-7170
Online Access:Get full text
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Summary:We consider the inverse sensitivity analysis problem of quantifying the uncertainty of inputs to a deterministic map given specified uncertainty in a linear functional of the output of the map. This is a version of the model calibration or parameter estimation problem for a deterministic map. We assume that the uncertainty in the quantity of interest is represented by a random variable with a given distribution, and we use the law of total probability to express the inverse problem for the corresponding probability measure on the input space. Assuming that the map from the input space to the quantity of interest is smooth, we solve the generally ill-posed inverse problem by using the implicit function theorem to derive a method for approximating the set-valued inverse that provides an approximate quotient space representation of the input space. We then derive an efficient computational approach to compute a measure theoretic approximation of the probability measure on the input space imparted by the approximate set-valued inverse that solves the inverse problem.
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ISSN:0036-1429
1095-7170
DOI:10.1137/100785946