An optimal pointwise weighted ensemble of surrogates based on minimization of local mean square error

Abstract

Surrogate models are often used as surrogates for computationally intensive simulations. And there are a variety of surrogate models which are widely used in aerospace engineering–related investigation and design. In general, there is an optimal individual surrogate for a certain research object. However, the behavior of an individual surrogate is unknown in advance. Building an ensemble of surrogates by combining different individual surrogates into a weighted-sum formulation is an efficient method to enhance the accuracy and robustness of the surrogate model. Motivated by the previous researches on the ensemble of surrogates, we propose an optimal pointwise weighted ensemble (OPWE) method, wherein the optimal pointwise weight factors are obtained based on the minimization of the local mean square error which is constructed by the global-local error (GLE). By using six well-known mathematical problems and four engineering problems, it is proved that the OPWE proposed in this paper is better than the other ensembles of surrogates in terms of both accuracy and robustness.