Numerical studies of space filling designs: optimization of Latin Hypercube Samples and subprojection properties

Guillaume Damblin (1) , Mathieu Couplet (1) , Bertrand Iooss (1, 2, 3)

1 EDF R&D STEP - Simulation et Traitement de l'information pour l'Exploitation des systèmes de Production
2 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
3 IMT - Institut de Mathématiques de Toulouse UMR5219

Quantitative assessment of the uncertainties tainting the results of computer simulations is nowadays a major topic of interest in both industrial and scientific communities. One of the key issues in such studies is to get information about the output when the numerical simulations are expensive to run. This paper considers the problem of exploring the whole space of variations of the computer model input variables in the context of a large dimensional exploration space. Various properties of space filling designs are justified: interpoint-distance, discrepancy, minimum spanning tree criteria. A specific class of design, the optimized Latin Hypercube Sample, is considered. Several optimization algorithms, coming from the literature, are studied in terms of convergence speed, robustness to subprojection and space filling properties of the resulting design. Some recommendations for building such designs are given. Finally, another contribution of this paper is the deep analysis of the space filling properties of the design 2D-subprojections.

Mots clés: discrepancy; optimal design; Latin Hypercube Sampling; computer experiment

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Guillaume Damblin, Mathieu Couplet, Bertrand Iooss. Numerical studies of space filling designs: optimization of Latin Hypercube Samples and subprojection properties. Journal of Simulation, 2013, 7, pp.276-289. ⟨hal-00848240⟩