Bounds on multivariate polynomials and exponential error estimates for multiquadratic interpolation
Journal of Approximation Theory
Algorithm 659: Implementing Sobol's quasirandom sequence generator
ACM Transactions on Mathematical Software (TOMS)
Design and Modeling for Computer Experiments (Computer Science & Data Analysis)
Design and Modeling for Computer Experiments (Computer Science & Data Analysis)
Maximin Latin Hypercube Designs in Two Dimensions
Operations Research
Discrete particle swarm optimization for constructing uniform design on irregular regions
Computational Statistics & Data Analysis
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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.