A Bayesian framework for functional calibration of expensive computational models through non-isometric matching
A Bayesian framework for functional calibration of expensive computational models through non-isometric matching
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DOI：
10.1080/24725854.2020.1774688
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发表时间：
2015-08
影响因子：
2.6
通讯作者：
Babak Farmanesh;Arash Pourhabib;Balabhaskar Balasundaram;Austin Buchanan
中科院分区：
文献类型：
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作者：
Babak Farmanesh;Arash Pourhabib;Balabhaskar Balasundaram;Austin Buchanan
摘要我们研究统计校准，即，调整计算模型的在其相关联的物理系统中不可观察或不可控制的特征。我们专注于功能校准，这是在许多制造过程中出现的不可观察的功能，称为校准变量，是输入变量的函数。在许多应用中的一个主要挑战是计算模型是昂贵的，只能评估有限的次数。此外，如果不进行强有力的假设，校准变量是不可识别的。我们提出了贝叶斯非等距匹配校准（BNMC），允许昂贵的计算模型的校准，只有有限数量的样本从计算模型及其相关的物理系统。BNMC用动态高斯过程代替计算模型，动态高斯过程的参数在校准过程中训练。为了解决可识别性问题，我们提出了从几何角度的非等距曲线曲面匹配的校准问题，这使我们能够利用组合优化技术来提取必要的信息，构建先验分布。我们的数值实验表明，在预测精度方面，BNMC优于，或与其他现有的校准框架。
Abstract We study statistical calibration, i.e., adjusting features of a computational model that are not observable or controllable in its associated physical system. We focus on functional calibration, which arises in many manufacturing processes where the unobservable features, called calibration variables, are a function of the input variables. A major challenge in many applications is that computational models are expensive and can only be evaluated a limited number of times. Furthermore, without making strong assumptions, the calibration variables are not identifiable. We propose Bayesian Non-isometric Matching Calibration (BNMC) that allows calibration of expensive computational models with only a limited number of samples taken from a computational model and its associated physical system. BNMC replaces the computational model with a dynamic Gaussian process whose parameters are trained in the calibration procedure. To resolve the identifiability issue, we present the calibration problem from a geometric perspective of non-isometric curve to surface matching, which enables us to take advantage of combinatorial optimization techniques to extract necessary information for constructing prior distributions. Our numerical experiments demonstrate that in terms of prediction accuracy BNMC outperforms, or is comparable to, other existing calibration frameworks.