Construction of uniform designs over continuous domain in computer experiments

Limited by practical operation, most experimental designs were constructed on discrete space, even if the influencing factors themselves are continuous. While in computer experiments, one can explore more possibilities to improve the modeling performance without increasing the test cost. As a space-filling design, the construction of uniform designs (UDs) can be naturally extended from lattice domain to continuous domain, so as to obtain better uniformity. In this article, coordinate descent methods are employed to construct UDs over the continuous domain with an initialization derived by threshold accepting (TA) algorithm. Our approach is suitable for arbitrary L-2-discrepancy. In particular, we provide the coordinate gradients under centered L-2-discrepancy and mixture discrepancy, as well as the code package. Computer experiments built on Kriging models show that our method can not only obtain more uniform designs, but also perform better in modeling than previous records.