大量输入计算机实验分析与建模的一种有效方法
An efficient methodology for the analysis and modeling of computer experiments with large number of inputs
摘要：
复杂的计算机代码通常太耗时，不能直接用于执行不确定性、灵敏度、优化和鲁棒性分析。一个被广泛接受的方法来规避这个问题，包括用cpu便宜的数学函数（称为元模型）代替cpu时间昂贵的计算机模型。例如，高斯过程（Gp）模型已经显示出解决实际问题的强大能力，通常涉及几个相互关联的问题。然而，在高维实验（通常有几十个输入）的情况下，Gp元模型的构建过程仍然很困难，甚至是不可行的，并且变量选择技术的应用无法避免。在本文中，我们提出了一个通用的方法，允许建立一个GP元模型，大量的投入，在一个非常有效的方式。虽然我们的工作集中在Gp元模型上，但它的原理是完全通用的，可以应用于任何类型的元模型。目标是双重的：从最少数量的计算机实验估计高度预测的元模型。该方法已成功地应用于工业计算机代码。
英文摘要：
Complex computer codes are often too time expensive to be directly used to perform uncertainty, sensitivity, optimization and robustness analyses. A widely accepted method to circumvent this problem consists in replacing cpu-time expensive computer models by cpu inexpensive mathematical functions, called metamodels. For example, the Gaussian process (Gp) model has shown strong capabilities to solve practical problems , often involving several interlinked issues. However, in case of high dimensional experiments (with typically several tens of inputs), the Gp metamodel building process remains difficult, even unfeasible, and application of variable selection techniques cannot be avoided. In this paper, we present a general methodology allowing to build a Gp metamodel with large number of inputs in a very efficient manner. While our work focused on the Gp metamodel, its principles are fully generic and can be applied to any types of metamodel. The objective is twofold: estimating from a minimal number of computer experiments a highly predictive metamodel. This methodology is successfully applied on an industrial computer code.
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