An Approach to Constructing Nested Space-Filling Designs for Multi-Fidelity Computer Experiments

Multi-fidelity computer experiments are widely used in many engineering and scientific fields. Nested space-filling designs (NSFDs) are suitable for conducting such experiments. Two classes of NSFDs are currently available. One class is based on special orthogonal arrays of strength two and the other consists of nested Latin hypercube designs. Both of them assume all factors are continuous. We propose an approach to constructing new NSFDs based on powerful (t, s)-sequences. The method is simple, easy to implement, and quite general. For continuous factors, this approach produces NSFDs with better space-filling properties than existing ones. Unlike the previous methods, this method can also construct NSFDs for categorical and mixed factors. Some illustrative examples are given. Other applications of the constructed designs are briefly discussed.