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Simulation-based optimal Bayesian experimental design for nonlinear systems

Author(s)
Huan, Xun; Marzouk, Youssef M.
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Abstract
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.
Date issued
2012-09
URI
http://hdl.handle.net/1721.1/99467
Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Journal
Journal of Computational Physics
Publisher
Elsevier
Citation
Huan, Xun, and Youssef M. Marzouk. “Simulation-Based Optimal Bayesian Experimental Design for Nonlinear Systems.” Journal of Computational Physics 232, no. 1 (January 2013): 288–317.
Version: Author's final manuscript
ISSN
00219991
1090-2716

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