Performances of Kriging on Several Industrial Case Studies: From Low to High Dimensional Hyperspaces
Celine Helbert, Delphine Dupuy
Laboratory Jean Kuntzmann, University Joseph Fourier, Grenoble, France, Metropolitan

Kriging is nowadays widely used to model expensive computer experiments. As a semi parametric method, kriging is expected to give better performances than poor flexible methods like linear models or too smooth methods like Multi Adaptive Regression Splines (MARS). Besides, kriging allows quantifying the prediction uncertainty which plays a major role in many applications such as uncertainty quantification or global optimization (EGO).

In this work, we propose to evaluate the quality of kriging in practice, from low to high dimensional cases, in different application fields (nuclear, energy, automobile, and aeronautic).

First, the panel of compared metamodels is briefly introduced. Secondly, we present a methodology for the evaluation and the comparison of metamodels results and illustrate it on a nuclear 3D application. Then, we show the good performances of kriging through a synthesis of results obtained on different industrial case studies. Moreover, the estimated ranges provide interesting information on the link between inputs and outputs. However, the well known underestimation of the prediction uncertainty of universal kriging is also observed in many cases. Finally, we show how Bayesian kriging is a good choice to enhance the accuracy of the prediction uncertainty and general performances of kriging, especially when an informative prior is obtained from industrial expertise.

Keywords: Computer experiments; Bayesian kriging; Metamodeling; Uncertainty quantification

Biography: Before joining the University Joseph Fourier of Grenoble in 2009, Celine Helbert worked during 5 years at the Ecole des Mines of Saint-Etienne, one of the best engineering schools in France where she took part in a reserch consortium on the analysis and the modeling of computer experiments. She worked on the evaluation and comparison of metamodels and especially on bayesian kriging, a good way to better quantify uncertainty. She now works in Grenoble on computer experiments handling spatiotemporal data.

The title of her today's talk is “Performances of kriging on several industrial case studies: from low to high dimensional hyperspaces”.