Regional error estimation of surrogates (REES)

Surrogate-based design is an effective approach for modeling computationally expensive system behavior. In such application, it is often challenging to characterize the expected accuracy of the surrogate. In addition to global and local error measures, regional error measures can be used to understand and interpret the surrogate accuracy in the regions of interest. This paper develops the Regional Error Estimation of Surrogate (REES) method to quantify the level of the error in any given subspace (or region) of the entire domain, when all the available training points have been invested to build the surrogate. In this approach, the accuracy of the surrogate in each subspace is estimated by modeling the variations of the mean and the maximum error in that subspace with increasing number of training points (in an iterative process). A regression model is used for this purpose. At each iteration, the intermediate surrogate is constructed using a subset of the entire train- ing data, and tested over the remaining points. The evaluated errors at the intermediate test points at each iteration are used for training the regression model that represents the error variation with sample points. The effectiveness of the proposed method is illustrated using standard test problems. To this end, the predicted regional errors of the surrogate constructed using all the training points are compared with the regional errors estimated over a large set of test points.