期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 232, 期 1, 页码 288-317出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2012.08.013
关键词
Uncertainty quantification; Bayesian inference; Optimal experimental design; Nonlinear experimental design; Stochastic approximation; Shannon information; Chemical kinetics
资金
- KAUST Global Research Partnership
- US Department of Energy, Office of Science, Office of Advanced Scientific Computing Research (ASCR) [DE-SC0003908]
The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general mathematical framework and an algorithmic approach for optimal experimental design with nonlinear simulation-based models; in particular, we focus on finding sets of experiments that provide the most information about targeted sets of parameters. Our framework employs a Bayesian statistical setting, which provides a foundation for inference from noisy, indirect, and incomplete data, and a natural mechanism for incorporating heterogeneous sources of information. An objective function is constructed from information theoretic measures, reflecting expected information gain from proposed combinations of experiments. Polynomial chaos approximations and a two-stage Monte Carlo sampling method are used to evaluate the expected information gain. Stochastic approximation algorithms are then used to make optimization feasible in computationally intensive and high-dimensional settings. These algorithms are demonstrated on model problems and on nonlinear parameter inference problems arising in detailed combustion kinetics. (C) 2012 Elsevier Inc. All rights reserved.
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