Gaussian process as complement to test functions for surrogate modeling

Abstract

It is common for papers on surrogate fitting to select test functions for testing algorithms. This raises the issue of how well the algorithms generalize to other functions. This editorial proposes as a possible complement to use a Gaussian process (GP) for generating test functions. The GP is defined by spatial decay rates of correlation between function values at different locations. The selection of these decay rates is tantamount to selection of the wave lengths of the functions that can be approximated by the surrogate. A possible complement to a given test function is a GP with similar decay rates to those of the test function, which would generate random functions with similar waviness. Two approaches are considered. In the simpler one, the GP is used to generate random test functions at a predetermined set of points. The more elaborate scheme targets situations where some samples are already available, and the GP is restricted to generate random functions that interpolate the samples. The process is illustrated for a one-dimensional case, where we seek to measure the correlation between the 95% confidence interval of the GP fit and the actual error. It is hoped that the editorial will stimulate discussion of the problem of algorithms customized to particular test functions and other options besides the one proposed here.