Simulation-based optimal Bayesian experimental design for nonlinear systems
Simulation-based optimal Bayesian experimental design for nonlinear systems
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DOI：
10.1016/j.jcp.2012.08.013
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发表时间：
2013-01-01
影响因子：
4.1
通讯作者：
Marzouk, Youssef M.
中科院分区：
文献类型：
--
作者：
Huan, Xun;Marzouk, Youssef M.
实验条件的最佳选择对于最大化用于推理和预测的数据的价值至关重要，特别是在进行实验既耗时又昂贵的情况下。我们提出了一个基于非线性模拟模型的最优实验设计的通用数学框架和算法方法，特别是，我们专注于寻找提供关于目标参数集的最多信息的实验集。我们的框架使用贝叶斯统计设置，这为从噪声、间接和不完整数据进行推理提供了基础，并提供了一种自然的机制来整合异质信息源。从信息论措施中构建目标函数，反映从拟议的实验组合中获得的预期信息收益。使用多项式混沌近似和两阶段蒙特卡罗抽样方法来估计期望信息增益。然后使用随机近似算法使优化在计算密集型和高维设置中可行。这些算法在模型问题和详细燃烧动力学中出现的非线性参数推断问题上都得到了验证。(C)2012 Elsevier Inc.保留所有权利。
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.