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arXiv 1912.07366stat.MLcs.LGstat.ME
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贝叶斯序贯优化设计从昂贵的黑盒函数中学习任意兴趣函数

Learning Arbitrary Quantities of Interest from Expensive Black-Box Functions through Bayesian Sequential Optimal Design

GE Research(通用电气研究中心);Purdue University(普渡大学)

Piyush Pandita, Nimish Awalgaonkar, Ilias Bilionis, Jitesh Panchal

摘要:

由于缺少领域知识和有限的预算,估计任意感兴趣的数量(QoI)是复杂的,昂贵的评估,黑盒函数的非线性算子是一个具有挑战性的问题。贝叶斯最优实验设计(Bayesian optimal design of experiments,BODE)是一种在不同背景下识别最优实验设计(optimal design of experiments,DOE)的方法,仅用于有限数量的函数评估。在BODE方法下,序贯实验设计(SDOE)通过选择最优的实验序列来完成这一任务,同时使用数据驱动的概率代理模型来代替昂贵的黑箱函数。从代理模型的概率预测被用来定义一个信息获取函数(IAF),它量化的边际值贡献或预期的信息获得一个假设的实验。通过最大化IAF来选择下一个实验。一般适用的IAF是关于QoI的预期信息增益(EIG),如通过在进行假设实验之后的QoI的预测分布与关于相同QoI的当前预测分布之间的库尔贝克-莱布勒散度的预期所捕获的。我们建模的基础信息源作为一个完全贝叶斯,非平稳的高斯过程(FBNSGP),并推导出一个近似的信息增益的假设实验的任意QoI条件下的超参数的EIG相同的QoI估计的样本平均值,以整合后验的超参数和潜在的实验结果。我们证明了我们的方法在四个数值例子和一个实际的工程问题的钢丝制造的性能。该方法进行了比较,两个经典的SDOE方法:随机抽样和不确定性抽样。

英文摘要:

Estimating arbitrary quantities of interest (QoIs) that are non-linear operators of complex, expensive-to-evaluate, black-box functions is a challenging problem due to missing domain knowledge and finite budgets. Bayesian optimal design of experiments (BODE) is a family of methods that identify an optimal design of experiments (DOE) under different contexts, using only in a limited number of function evaluations. Under BODE methods, sequential design of experiments (SDOE) accomplishes this task by selecting an optimal sequence of experiments while using data-driven probabilistic surrogate models instead of the expensive black-box function. Probabilistic predictions from the surrogate model are used to define an information acquisition function (IAF) which quantifies the marginal value contributed or the expected information gained by a hypothetical experiment. The next experiment is selected by maximizing the IAF. A generally applicable IAF is the expected information gain (EIG) about a QoI as captured by the expectation of the Kullback-Leibler divergence between the predictive distribution of the QoI after doing a hypothetical experiment and the current predictive distribution about the same QoI. We model the underlying information source as a fully-Bayesian, non-stationary Gaussian process (FBNSGP), and derive an approximation of the information gain of a hypothetical experiment about an arbitrary QoI conditional on the hyper-parameters The EIG about the same QoI is estimated by sample averages to integrate over the posterior of the hyper-parameters and the potential experimental outcomes. We demonstrate the performance of our method in four numerical examples and a practical engineering problem of steel wire manufacturing. The method is compared to two classic SDOE methods: random sampling and uncertainty sampling.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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