An adaptive sampling approach for Kriging metamodeling by maximizing expected prediction error

- A novel adaptive sampling approach for Kriging metamodeling via maximizing expected prediction error is proposed.
- Under the bias-variance framework, it uses cross-validation to conduct local exploitation in regions with large prediction errors.
- It uses an adaptive balance strategy to dynamically balance local exploitation and global exploration.
- Numerical results reveal that this approach can build more accurate Kriging models with the same number of sample points.

As a well-known approximation method, Kriging is widely used in process engineering design and optimization for saving computational budget. The Kriging model for a target function is fitted to a set of sample points, the responses of which are expensive to obtain in practice and the sample distribution of which has a great impact on the model prediction quality. Therefore, a main task in adaptive sampling for Kriging metamodeling is to gather informative points in order to build an accurate model with as few points as possible. To this end, we propose an adaptive sampling approach under the bias-variance decomposition framework. This novel sampling approach sequentially selects new points by maximizing an expected prediction error criterion that considers both the bias and variance information. Particularly, it presents an adaptive balance strategy to dynamically balance the local exploitation and global exploration via the error information from the previous iteration. Four benchmark cases and four engineering cases from low to high dimensions are used to assess the performance of the proposed approach. Numerical results reveal that this adaptive sampling approach is very promising for constructing accurate Kriging models for problems with diverse characteristics.