标题： 具有多保真度的计算机实验递归共克里金模型及其在水动力学中的应用 显示英文标题

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

摘要： 在许多实际情况下，对一个复杂且耗时的计算机代码进行敏感性分析或优化需要构建一个快速运行的近似模型——也称为代理模型。本文考虑了构建复杂计算机代码代理模型的问题，该代码可以在不同的精度水平下运行。基于共克里金法的代理模型是一种很有前景的工具来构建这种近似。 其想法是利用快速但准确性较低的代码版本来改进代理模型。这里我们提出了一种新的方法来执行多保真共克里金模型，该方法基于递归公式。这种方法的优点在于共克里金模型通过一系列独立的克里金模型构建而成。由此可以自然地将经典克里金模型的一些性质扩展到提出的共克里金模型中，例如快速交叉验证过程。此外，基于贝叶斯线性公式，提供了共克里金模型的通用克里金方程扩展形式。最后，与之前的模型相比，所提出的模型具有降低计算复杂性的优势。多保真模型成功应用于水动力模拟器的仿真。这个真实案例展示了递归模型的有效性。 显示英文摘要

摘要： 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.