In many practical cases, a sensitivity analysis or an optimization of a
complex time consuming computer code requires to build a fast running
approximation of it - also called surrogate model. We consider in this paper
the problem of building a surrogate model of a complex computer code which can
be run at different levels of accuracy. The co-kriging based surrogate model is
a promising tool to build such an approximation. The idea is to improve the
surrogate model by using fast and less accurate versions of the code. We
present here a new approach to perform a multi-fidelity co-kriging model which
is based on a recursive formulation. The strength of this new method is that
the co-kriging model is built through a series of independent kriging models.
From them, some properties of classical kriging models can naturally be
extended to the presented co-kriging model such as a fast cross-validation
procedure. Moreover, based on a Bayes linear formulation, an extension of the
universal kriging equations are provided for the co-kriging model. Finally, the
proposed model has the advantage to reduce the computational complexity
compared to the previous models. The multi-fidelity model is successfully
applied to emulate a hydrodynamic simulator. This real example illustrates the
efficiency of the recursive model.

本文提出了一种基于递归公式的多保真度联合克里金模型，其优点在于该模型通过一系列独立的克里金模型来建立，可以自然地扩展一些传统克里金模型的属性，同时提供了一种通用克里金方程的扩展方法，成功应用于仿真程序的建模，降低了计算复杂度。

多保真度计算机实验设计的递归共同克里金模型及其在流体力学中的应用

Recursive co-kriging model for Design of Computer experiments with  multiple levels of fidelity with an application to hydrodynamic

Gaussian process models -also called Kriging models- are often used as
mathematical approximations of expensive experiments. However, the number of
observation required for building an emulator becomes unrealistic when using
classical covariance kernels when the dimension of input increases. In oder to
get round the curse of dimensionality, a popular approach is to consider
simplified models such as additive models. The ambition of the present work is
to give an insight into covariance kernels that are well suited for building
additive Kriging models and to describe some properties of the resulting
models.

本文旨在探讨适用于构建加法 Kriging 模型的协方差核，并描述所得模型的一些特性。