Surrogate models are useful in a wide variety of engineering applications. The employment of these computationally efficient surrogates for complex physical models offers a dramatic reduction in the computational effort required to conduct analyses for the purpose of engineering design. In order to realize this advantage, it is necessary to “fit” the surrogate model to the underlying physical model. This is a considerable challenge as the physical model may consist of many design variables and performance indices, exhibit nonlinear and/or mixed-discrete behaviors, and is typically expensive to evaluate. As a result adaptive sequential sampling techniques, where previous evaluations of the physical model dictate subsequent sample locations, are widely used. In this work, we develop and demonstrate a novel adaptive sequential sampling algorithm for fitting surrogate models of any type, with a focus on large data sets. By examining the monotonicity of an error function the design space is repeatedly partitioned in order to compute a set of “key points.” The key points reduce the problem of fitting to one of precise interpolation, which can be accomplished using well-known methods. We demonstrate the use of this technique to fit several surrogate model types, including blended Hermitian polynomials and Non-Uniform Rational B-splines (NURBs), to nonlinear noisy data. We conclude with our observations as to the effectiveness of this fitting technique, its strengths and limitations, as well as a discussion of further work in this vein.
Outlier eigenvalues for non-Hermitian polynomials in independent i.i.d. matrices and deterministic matrices