Statistics and Computing

, Volume 22, Issue 3, pp 703–712 | Cite as

Maximin design on non hypercube domains and kernel interpolation

  • Yves Auffray
  • Pierre Barbillon
  • Jean-Michel Marin
Article

Abstract

In the paradigm of computer experiments, the choice of an experimental design is an important issue. When no information is available about the black-box function to be approximated, an exploratory design has to be used. In this context, two dispersion criteria are usually considered: the minimax and the maximin ones. In the case of a hypercube domain, a standard strategy consists of taking the maximin design within the class of Latin hypercube designs. However, in a non hypercube context, it does not make sense to use the Latin hypercube strategy. Moreover, whatever the design is, the black-box function is typically approximated thanks to kernel interpolation. Here, we first provide a theoretical justification to the maximin criterion with respect to kernel interpolations. Then, we propose simulated annealing algorithms to determine maximin designs in any bounded connected domain. We prove the convergence of the different schemes. Finally, the methodology is applied on a challenging real example where the black-blox function describes the behaviour of an aircraft engine.

Keywords

Computer experiments Kernel interpolation Kriging maximin designs Simulated annealing 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Yves Auffray
    • 1
  • Pierre Barbillon
    • 2
  • Jean-Michel Marin
    • 3
  1. 1.Dassault Aviation & Département de MathématiquesUniversité Paris-SudOrsayFrance
  2. 2.INRIA Saclay, Projet Select, Département de MathématiquesUniversité Paris-SudOrsayFrance
  3. 3.Institut de Mathématiques et Modélisation de MontpellierUniversité Montpellier 2Montpellier cedex 5France

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