Toward an optimal ensemble of kernel-based approximations with engineering applications

This paper presents a general approach toward the optimal selection and ensemble (weighted average) of kernel-based approximations to address the issue of model selection. That is, depending on the problem under consideration and loss function, a particular modeling scheme may outperform the others, and, in general, it is not known a priori which one should be selected. The surrogates for the ensemble are chosen based on their performance, favoring non-dominated models, while the weights are adaptive and inversely proportional to estimates of the local prediction variance of the individual surrogates. Using both well-known analytical test functions and, in the surrogate-based modeling of a field scale alkali-surfactant-polymer enhanced oil recovery process, the ensemble of surrogates, in general, outperformed the best individual surrogate and provided among the best predictions throughout the domains of interest. This work was supported in part by the Fondo Nacional de Ciencia, Tecnología e Innovación (FONACIT), Venezuela under Grant F-2005000210. N. Q. Author also acknowledges that this material is based upon work supported by National Science Foundation under Grant DDM-423280.