Sequential Experimental Designs for Kriging Model

2026-01-23

AI Summary

This study addresses key limitations in existing sequential experimental design strategies for Kriging models, including low information utilization in single-point approaches, insufficient research on batch strategies, and the tendency of sampling points to cluster. To overcome these issues, the authors propose two novel single-point sequential criteria and develop a general-purpose batch sequential design framework that, for the first time, enables efficient extension of arbitrary sequential criteria to batch settings. The framework effectively mitigates point clustering and substantially enhances both information utilization efficiency and experimental cycle effectiveness. Numerical experiments based on Kriging surrogate models demonstrate that the proposed methods consistently outperform state-of-the-art approaches across multiple benchmark functions, achieving superior approximation accuracy and computational efficiency.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Sequential Decision Making
• Machine Learning: Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Computer experiments have become an indispensable alternative to complex physical and engineering experiments. The Kriging model is the most widely used surrogate model, with the core goal of minimizing the discrepancy between the surrogate and true models across the entire experimental domain. However, existing sequential design methods have critical limitations: observation-based batch sequential designs are rarely studied, while one-point sequential designs have insufficient information utilization and suffer from inefficient resource utilization -- they require numerous repeated observation rounds to accumulate sufficient points, leading to prolonged experimental cycles. To address these gaps, this paper proposes two novel one-point sequential design criteria and a general batch sequential design framework. Moreover, the batch sequential design framework solves the inherent point clustering problem in naive batch selection, enabling efficient extension of any sequential criterion to batch scenarios. Simulations on some test functions demonstrate that the proposed methods outperform existing approaches in terms of fitting accuracy in most cases.

Problem

• Sequential Experimental Design
• Kriging Model
• Batch Selection
• Point Clustering
• Surrogate Modeling

Innovation

• sequential design
• Kriging model
• batch sampling
• point clustering
• surrogate modeling