Constructing orthogonal maximin distance uniform projection designs for computer experiments

There is a significant need for computer experiments to study and model complex physical systems. In both computer and physical experiments, constructing experimental designs with good space-filling and column-orthogonality properties is crucial. While maximin distance designs and uniform designs ensure space-filling in full-dimensional spaces, they lack guarantees for low-dimensional projections. Uniform projection designs address this gap by ensuring space-filling properties in low-dimensional subspaces. Orthogonal designs enable efficient factor screening in Gaussian processes and ensure uncorrelated estimates of main effects in linear models. However, constructing such optimal designs remains challenging. A design that combines these advantages would outperform individual approaches. This paper fills this gap by proposing seven novel theoretical techniques for constructing orthogonal maximin distance uniform projection designs. The proposed designs demonstrate superior performance as the number of factors increases, making them particularly well-suited for surrogate modeling and linear trend estimation in high-dimensional Gaussian processes. Comparative studies show that the proposed techniques outperform existing methods.