Quantifying Regional Error in Surrogates by Modeling its Relationship with Sample Density

Approximation models (or surrogate models) provide an efficient substitute to expen-sive physical simulations and an efficient solution to the lack of physical models of system behavior. However, it is challenging to quantify the accuracy and reliability of such ap-proximation models in a region of interest or the overall domain without additional system evaluations. Standard error measures, such as the mean squared error, the cross-validation error, and the Akaikes information criterion, provide limited (often inadequate) informa-tion regarding the accuracy of the final surrogate. This paper introduces a novel and model independent concept to quantify the level of errors in the function value estimated by the final surrogate in any given region of the design domain. This method is called the Re-gional Error Estimation of Surrogate (REES). Assuming the full set of available sample points to be fixed, intermediate surrogates are iteratively constructed over a sample set comprising all samples outside the region of interest and heuristic subsets of samples inside the region of interest (i.e., intermediate training points). The intermediate surrogate is tested over the remaining sample points inside the region of interest (i.e., intermediate test points). The fraction of sample points inside region of interest, which are used as interme