Radial basis functions for multivariable interpolation: a review
Algorithms for approximation
Applications of machine learning and rule induction
Communications of the ACM
Neural Networks for Pattern Recognition
Neural Networks for Pattern Recognition
State-of-the-Art Review: A User's Guide to the Brave New World of Designing Simulation Experiments
INFORMS Journal on Computing
A study of cross-validation and bootstrap for accuracy estimation and model selection
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
An adaptive hybrid surrogate model
Structural and Multidisciplinary Optimization
Performance of an ensemble of ordinary, universal, non-stationary and limit Kriging predictors
Structural and Multidisciplinary Optimization
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Surrogate models are often used to replace expensive simulations of engineering problems. The common approach is to construct a series of metamodels based on a training set, and then, from these surrogates, pick out the best one with the highest accuracy as an approximation of the computationally intensive simulation. However, because the choice of approximate model depends on design of experiments (DOEs), the traditional strategy thus increases the risk of adopting an inappropriate model. Furthermore, in the design of complex product system, because of its feature of one-of-a-kind production, acquiring more samples is very expensive and intensively time-consuming, and sometimes even impossible. Therefore, in order to save sampling cost, it is a reasonable strategy to take full advantage of all the stand-alone surrogates and then combine them into an ensemble model. Ensemble technique is an effective way to make up for the shortfalls of traditional strategy. Motivated by the previous research on ensemble of surrogates, a new technique for constructing of a more accurate ensemble of surrogates is proposed in this paper. The weights are obtained using a recursive process, in which the values of these weights are updated in each iteration until the last ensemble achieves a desirable prediction accuracy. This technique has been evaluated using five benchmark problems and one reality problem. The results show that the proposed ensemble of surrogates with recursive arithmetic average provides more ideal prediction accuracy than the stand-alone surrogates and for most problems even exceeds the previously presented ensemble techniques. Finally, we should point out that the advantages of combination over selection are still difficult to illuminate. We are still using an "insurance policy" mode rather than offering significant improvements.