Sliced rotated sphere packing designs

TL;DR

This paper introduces sliced rotated sphere packing designs, a new class of space-filling designs for computer experiments, with algorithms for their construction and an adaptive strategy for efficient exploration.

Contribution

It proposes sliced rotated sphere packing designs, combining rotated sphere packing designs with slicing, and provides algorithms and an adaptive strategy for their application.

Findings

Designs are constructed via rescaling, rotating, translating, and slicing lattice points.

Algorithms enable fast generation of these designs.

Adaptive strategy improves local space-filling properties.

Abstract

Space-filling designs are popular choices for computer experiments. A sliced design is a design that can be partitioned into several subdesigns. We propose a new type of sliced space-filling design called sliced rotated sphere packing designs. Their full designs and subdesigns are rotated sphere packing designs. They are constructed by rescaling, rotating, translating and extracting the points from a sliced lattice. We provide two fast algorithms to generate such designs. Furthermore, we propose a strategy to use sliced rotated sphere packing designs adaptively. Under this strategy, initial runs are uniformly distributed in the design space, follow-up runs are added by incorporating information gained from initial runs, and the combined design is space-filling for any local region. Examples are given to illustrate its potential application.