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

2025-05-14

AI Summary

This paper addresses the challenge of constructing space-filling designs for computer experiments under high-dimensional and constrained settings, aiming to enhance prediction accuracy and uncertainty quantification—particularly for Gaussian process (GP) surrogates. We systematically analyze the theoretical connections between space-filling criteria (e.g., Maximin, Latin hypercube, projection-based designs) and GP performance, establishing—for the first time—a rigorous link between fill distance and predictive error bounds. We further propose failure criteria for design construction in high-dimensional and constrained scenarios and identify the convergence of adaptive sampling with machine learning as a key evolutionary direction. Through comprehensive numerical experiments, we quantitatively evaluate trade-offs among accuracy, robustness, and computational cost across design families. Results confirm that fill distance serves as a strong indicator of surrogate generalization capability. The work delivers interpretable, reusable design principles for digital twin and cyber-physical systems.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Reviewing space-filling designs for accurate surrogate modeling
• Connecting design criteria to Gaussian process performance
• Exploring trade-offs and challenges in high-dimensional settings

Innovation

• Space-filling designs for efficient computer experiments
• Review of Maximin, Latin hypercubes, projection designs
• Link design criteria to Gaussian process performance