High dimensional Kriging metamodelling utilising gradient information

• GEK-HDMR approach is proposed to tackle ‘curse-of-dimensionality in HD problems.
• LOLA-Voronoi adaptive sampling scheme is integrated with GEK-HDMR.
• Additional gradient data incorporation in Kriging-based HD modeling is introduced.
• Training data required to model HD problems is significantly reduced.
• GEK and HDMR can be sufficient to break or attenuate the “curse of dimensionality”.

Kriging-based metamodels are popular for approximating computationally expensive black-box simulations, but suffer from an exponential growth of required training samples as the dimensionality of the problem increases. While a Gradient Enhanced Kriging metamodel with less training samples is able to approximate more accurately than a Kriging-based metamodel, it is prohibitively expensive to build for high dimensional problems. This limits the applicability of Gradient Enhanced Kriging for high dimensional metamodelling. In this work, this limitation is alleviated by coupling Gradient Enhanced Kriging with High Dimensional Model Representation. The approach, known as Gradient Enhanced Kriging based High Dimensional Model Representation, is accompanied by a highly efficient sequential sampling scheme LOLA-Voronoi and is applied to various high dimensional benchmark functions and one real-life simulation problem of varying dimensionality (10D–100D). Test results show that the combination of inexpensive gradient information and the high dimensional model representation can break or at least loosen the limitations associated with high dimensional Kriging metamodelling.