Design of Experiments for Emulations: A Selective Review from a Modeling Perspective

TL;DR

This paper reviews key space-filling design methodologies for computer experiments, analyzing their theoretical properties, practical trade-offs, and future directions in adaptive sampling and machine learning integration.

Contribution

It provides a comprehensive review of design strategies like Maximin, Latin hypercubes, and connects design criteria to Gaussian process performance, highlighting challenges and future research directions.

Findings

Numerical studies on design trade-offs in high-dimensional settings

Connections between fill distance and Gaussian process accuracy

Discussion on challenges in constrained and adaptive designs

Abstract

Space-filling designs are crucial for efficient computer experiments, enabling accurate surrogate modeling and uncertainty quantification in many scientific and engineering applications, such as digital twin systems and cyber-physical systems. In this work, we will provide a comprehensive review on key design methodologies, including Maximin/miniMax designs, Latin hypercubes, and projection-based designs. Moreover, we will connect the space-filling design criteria like the fill distance to Gaussian process performance. Numerical studies are conducted to investigate the practical trade-offs among various design types, with the discussion on emerging challenges in high-dimensional and constrained settings. The paper concludes with future directions in adaptive sampling and machine learning integration, providing guidance for improving computational experiments.