A comparative study between kriging and adaptive sparse tensor-product methods for multi-dimensional approximation problems in aerodynamics design*

Abstract

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.