A numerical method for solving a stochastic inverse problem for parameters

被引:6
|
作者
Butler, T. [1 ]
Estep, D. [2 ]
机构
[1] Univ Texas Austin, Inst Computat Engn & Sci, Austin, TX 78712 USA
[2] Colorado State Univ, Dept Stat, Ft Collins, CO 80523 USA
基金
美国国家科学基金会; 美国国家卫生研究院; 美国国家航空航天局;
关键词
A posteriori error analysis; Adjoint problem; Density estimation; Inverse sensitivity analysis; Nonparametric density estimation; Sensitivity analysis; NONPARAMETRIC DENSITY-ESTIMATION; UNCERTAIN PARAMETERS; EVOLUTION;
D O I
10.1016/j.anucene.2012.05.016
中图分类号
TL [原子能技术]; O571 [原子核物理学];
学科分类号
0827 ; 082701 ;
摘要
We review recent work (Briedt et al., 2011, 2012) on a new approach to the formulation and solution of the stochastic inverse parameter determination problem, i.e. determine the random variation of input parameters to a map that matches specified random variation in the output of the map, and then apply the various aspects of this method to the interesting Brusselator model. In this approach, the problem is formulated as an inverse problem for an integral equation using the Law of Total Probability. The solution method employs two steps: (1) we construct a systematic method for approximating set-valued inverse solutions and (2) we construct a 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. In addition to convergence analysis, we carry out an a posteriori error analysis on the computed probability distribution that takes into account all sources of stochastic and deterministic error. (C) 2012 Elsevier Ltd. All rights reserved.
引用
收藏
页码:86 / 94
页数:9
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