Construction of space-filling designs using WSP algorithm for high dimensional spaces

In the computer experiments setting, if the relationship between the response and the inputs is unknown, then the purpose is to use designs that spread the points at which the response is observed evenly throughout the region. These designs are called space-filling designs (SFD) and the most known are Latin Hypercubes (random, orthogonal, optimized) and low discrepancy sequences. But, simulation codes becoming more and more complex, high dimensional optimal designs are needed to study a high number of parameters (more than 20 parameters) and the construction proves difficult. The aim of this study is to explore a construction method of new space-filling designs for high dimensional spaces. After a short presentation of the criteria considered to quantify the intrinsic quality of the designs, the generation of these designs using WSP algorithm is presented. As the first step consists in generating candidate points, the influence of the initial set of points is investigated in dimension 20 and the final designs are compared with others space-filling designs. Then, designs are proposed in dimension 20, 30, 40 and 50 and the study of the intrinsic quality of these new space-filling designs highlights the robustness of this generation method in high dimensional spaces.