| Issue |
ESAIM: Proc.
Volume 48, January 2015
CEMRACS 2013 - Modelling and simulation of complex systems: stochastic and deterministic approaches
|
|
|---|---|---|
| Page(s) | 248 - 261 | |
| DOI | https://doi.org/10.1051/proc/201448011 | |
| Published online | 09 March 2015 | |
A comparative study between kriging and adaptive sparse tensor-product methods for multi-dimensional approximation problems in aerodynamics design*
1 LJLL, Université Pierre &
Marie Curie, 75005,
Paris,
France
2 Onera, The French Aerospace Lab.
92322
Châtillon,
France
The performances of two multivariate interpolation procedures are compared using functions that are either synthetic or coming from a shape optimization problem in aerodynamics. The aim is to evaluate the efficiency of adaptive sparse interpolation algorithms 2 and compare them with the kriging approach developed for the design and analysis of computer experiment (DACE) 21. The accuracy and computational time of the two methods are examined as the number N of samples used in the interpolation increases. It appears in our test cases that both methods perform equivalently, in terms of precision. However, as the dimension d increases, the computational time involved in the enrichement of the kriging sample becomes intractable for large values of N. This problem is circumvented in the case of the sparse interpolation procedure for which the computational time scales linearly with N and d.
Résumé
Nous comparons les performances de deux méthodes d’interpolation en grande dimension, aussi bien sur des fonctions synthétiques que pour celles issues d’un problème d’optimisation de forme en aerodynamique. L’objectif est d’évaluer l’efficacité d’algorithmes adaptatifs d’interpolation parcimonieuse 2, et de les comparer avec l’approche du kriging développée dans le cadre design and analysis of computer experiment (DACE) 21. La précision et le temps de calcul des deux méthodes sont étudiés lorsque le nombre N d’échantillons utilisés pour l’interpolation augmente. Les cas tests montrent que les deux méthodes sont comparables en terme de précision. Cependant, lorsque la dimension d augmente, le temps de calcul associé à l’enrichissement de l’échantillon pour le kriging devient prohibitif pour les grandes valeurs de N. Ce problème est contourné dans le cas de l’interpolation parcimonieuse pour lequel le temps de calcul est linéaire en N et d.
© EDP Sciences, SMAI 2015
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