Simulation-based optimal Bayesian experimental design for nonlinear systems
AbstractThe 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. © 2012 Elsevier Inc.
CitationHuan X, Marzouk YM (2013) Simulation-based optimal Bayesian experimental design for nonlinear systems. Journal of Computational Physics 232: 288–317. Available: http://dx.doi.org/10.1016/j.jcp.2012.08.013.
SponsorsThe authors would like to acknowledge support from the KAUST Global Research Partnership and from the US Department of Energy, Office of Science, Office of Advanced Scientific Computing Research (ASCR) under Grant No. DE-SC0003908.
JournalJournal of Computational Physics