标题： 一种用于通过非等距匹配对昂贵计算模型进行功能校准的贝叶斯框架 显示英文标题

标题： A Bayesian framework for functional calibration of expensive computational models through non-isometric matching

摘要： 我们研究了统计校准，即调整计算模型中与其相关物理系统中不可观测或不可控的特征。我们重点关注功能校准，它出现在许多制造过程中，其中不可观测的特征（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，计算模型昂贵且只能有限次数地进行评估。此外，在不做强假设的情况下，校准变量不可识别。我们提出了贝叶斯非等距匹配校准（BNMC），该方法允许使用从计算模型及其相关物理系统中采样的有限样本对昂贵的计算模型进行校准。BNMC用动态高斯过程（GP）替换计算模型，其参数在校准过程中进行训练。为了解决可识别性问题，我们从非等距曲线到曲面匹配的几何角度提出了校准问题，这使我们能够利用组合优化技术提取构建先验分布所需的必要信息。我们的数值实验表明，就预测准确性而言，BNMC优于或至少与其他现有校准框架相当。 显示英文摘要

摘要： 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 (GP) 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.