Performance assessment of a cross-validation sampling strategy with active surrogate model selection

Surrogate Models (SM) are now regarded as powerful tools for engineering design applications; they approximate expensive responses obtained by either a computer simulation or a real experiment with more computationally efficient mathematical models. The goal of reducing the number of function evaluations required to create the training dataset led to the development of strategies capable of effectively sampling the design space. In particular, sequential adaptive techniques seem to be the most promising approaches for engineering design applications. Unfortunately, most of these techniques supervise the sampling phase with an SM created from the available training set, making their behavior dependent on the chosen SM formulation. This characteristic can cause sampling performance deterioration, in particular when an inaccurate SM formulation is used to supervise the sampling process. The solution proposed in this paper tries to mitigate this problem by coupling the model-dependent sequential adaptive technique with an active SM selection approach. This surrogate modeling architecture is tested on several example functions, and results indicate that it inherits the advantages of both constituent elements: an increased flexibility due to the active SM selection and a reduced total number of samples due to the sequential adaptive sampling strategy. Other parameters which may affect the sampling performance (such as the SM selection frequency and criterion) are also analyzed in an attempt to define general guidelines for the application of the method. The sampling technique considered in this study is based on cross-validation variance, and the surrogate modeling performance is assessed on nine two-dimensional and two five-dimensional test functions.