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

Abstract

This paper presents a general approach toward the optimal selection and ensemble (weighted average) of surrogates (kernel-based approximations) to address the issue of model uncertainty (model selection); that is, depending on the problem under consideration and loss function (i.e., quadratic, Laplace, e-insensitive) a particular modeling scheme (e.g., polynomial regression, splines, Gaussian radial basis functions, or kriging) 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 (ASP) enhanced oil recovery process, the ensemble of surrogates, in general, outperformed (i.e., mean error, standard deviation, and maximum absolute error) the best individual surrogate and provided among the best predictions throughout the domains of interest.