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

作者：Breidt J^*; Butler T; Estep D

来源：SIAM Journal on Numerical Analysis, 2011, 49(5): 1836-1859.

DOI：10.1137/100785946

• adjoint problem
• density estimation
• inverse sensitivity analysis
• model calibration
• nonparametric density estimation
• parameter estimation
• sensitivity analysis
• set-valued inverse

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.

• 出版日期2011