Comparative studies of support vector regression and kriging — theory and applications

Support vector regression, as one of most promising surrogate modeling methods, has good capability of filtering numerical noise and is well suited for surrogate modeling problems with high nonlinearity. In this paper, least square SVR (LS-SVR) is further derived and it is found that the formulation of the LS-SVR predictor looks almost same as that of Kriging revised for regression. Then couples of numerical examples with or without numerical noises are used for comparing these two surrogate models. It is found that SVR shows better global fitting ability and behaves more robust when numerical noises exist. Two sampling methods, uniform sampling, as well as LHS (Latin Hypercube Sampling) for initial sampling and MSP+EI (MSP: minimizing surrogate prediction, EI: maximizing the expected improvement) for infilling new samples, are compared in some examples. From the preliminary comparisons it is concluded that LS-SVR has an apparent advantage over Kriging when the samples are limited and uniformly distributed. Kriging behaves better and has comparative accuracy with LS-SVR when the LHS sampling and MSP+EI criteria are applied.