Distance correlation-based nearly orthogonal space-filling experimental designs

In many real-world applications of optimisation, the required model (function) evaluations are determined by expensive and time-consuming physical experiments or numerical procedures. Within this context, the objective of experimental design is to obtain meaningful information based on a strongly limited number of experiments or function evaluations. In order to generate informative designs, space-filling and orthogonality are widely considered to be essential. In this study, we review several existing design performance metrics that address these criteria, and the distance correlation-based metric is proposed for achieving improved experimental design. Three closely related randomised sampling schemes are proposed to generate nearly orthogonal designs with good space-filling properties in real time. The effectiveness of our approach is demonstrated by numerical examples and an illustrative borehole model case study.