Construction of nested space-filling designs

TL;DR

This paper introduces nested space-filling designs for multi-level computer experiments, developing new construction methods and mathematical concepts like nested orthogonal arrays and difference matrices.

Contribution

It presents novel approaches to constructing nested space-filling designs and introduces new discrete mathematics concepts for this purpose.

Findings

Developed multiple methods for constructing nested space-filling designs.

Introduced new concepts: nested orthogonal arrays and nested difference matrices.

Enhanced the toolkit for multi-level computer experiment design.

Abstract

New types of designs called nested space-filling designs have been proposed for conducting multiple computer experiments with different levels of accuracy. In this article, we develop several approaches to constructing such designs. The development of these methods also leads to the introduction of several new discrete mathematics concepts, including nested orthogonal arrays and nested difference matrices.