Fully-sequential space-filling design algorithms for computer experiments

Fully-sequential (i.e., with design points added one-at-a-time) space-filling designs are useful for global surrogate modeling of expensive computer experiments when the number of design points required to achieve a suitable accuracy is unknown in advance. We develop and investigate three fully-sequential space-filling (FSSF) design algorithms that are conceptually simple and computationally efficient and that achieve much better space-filling properties than alternative methods such as Sobol sequences and more complex batch-sequential methods based on sliced or nested optimal Latin hypercube designs (LHDs). Remarkably, at each design size in the sequence, our FSSF algorithms even achieve much better space-filling properties than a one-shot LHD optimized for that specific size. The algorithms we propose also scale well to very large design sizes. We provide an R package to implement the approaches.