Ensemble of Kriging with Multiple Kernel Functions for Engineering Design Optimization

Abstract

We introduce the ensemble of Kriging with multiple kernel functions guided by cross-validation error for creating a robust and accurate surrogate model to handle engineering design problems. By using the ensemble of Kriging models, the resulting ensemble model preserves the uncertainty structure of Kriging, thus, can be further exploited for Bayesian optimization. The objective of this paper is to develop a Kriging methodology that eliminates the needs for manual kernel selection which might not be optimal for a specific application. Kriging models with three kernel functions, that is, Gaussian, Matérn-3/2, and Matérn-5/2 are combined through a global and a local ensemble technique where their approximation quality are investigated on a set of aerodynamic problems. Results show that the ensemble approaches are more robust in terms of accuracy and able to perform similarly to the best performing individual kernel function or avoiding misspecification of kernel.