Simulation-based optimal Bayesian experimental design for nonlinear systems

By Xun Huan, Youssef M. Marzouk. Journal of Computational Physics, 2011

482 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b4f48369aec6ecea27c6013f37e0ad8eeba5f614

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Citations in the corpus

A Review of Modern Computational Algorithms for Bayesian Optimal Design (2016, methodology): “Huan and Marzouk (2012, 2013) used polynomial chaos approximations and nested Monte Carlo integration (Ryan [2003]) to estimate the KLD between the prior and posterior distributions for static design problems for parameter estimation.”