多精度计算机试验的高维代理模型
High-Dimensional Surrogate Modeling for Multi-Fidelity Computer Experiments
DOI: 10.12677/sa.2025.148235, PDF,    科研立项经费支持
作者: 陈 璇：国防科技大学理学院，湖南 长沙；崔 婷：中国科学院大学数学科学学院，北京；中国科学院数学与系统科学研究院，北京；吕 磊：南京电子设备研究所，江苏 南京；黄思源*：北京工业大学数学统计学与力学学院，北京
关键词: 多精度计算机试验；高斯过程回归；变换可加高斯过程；嵌套拉丁超立方设计；Multi-Fidelity Computer Experiments； Gaussian Process Regression； Transformation Additive Gaussian Process； Nested Latin Hypercube Design
摘要: 多精度计算机试验结合不同精度的数据，以降低计算成本并提高预测精度。然而，在高维问题中，传统方法面临计算复杂度高、数据稀疏性强等挑战。本文提出一种基于变换可加高斯(TAG)过程的高维多精度代理模型，并结合嵌套设计，在精度层级间构建层级化误差修正关系。该方法有效提升了高维情形下的建模精度和计算效率。数值实验表明，本文提出的方法在高维问题中优于传统的多精度高斯过程模型，适用于高维情形下的多精度计算机试验的代理建模。
Abstract: Multi-fidelity computer experiments integrate data of varying fidelity levels to reduce computational costs and improve prediction accuracy. However, traditional methods face challenges in high-dimensional problems due to high computational complexity and severe data sparsity. This paper proposes a high-dimensional multi-fidelity surrogate model based on the transformation additive Gaussian (TAG) process and incorporates the nested design to establish a hierarchical error correction relationship. The proposed approach effectively enhances modeling accuracy and computational efficiency in high-dimensional cases. Numerical experiments demonstrate that this method outperforms traditional multi-fidelity Gaussian process models in high-dimensional settings, making it well-suited for surrogate modeling of high-dimensional multi-fidelity computer experiments.
文章引用：陈璇, 崔婷, 吕磊, 黄思源. 多精度计算机试验的高维代理模型[J]. 统计学与应用, 2025, 14(8): 284-296. https://doi.org/10.12677/sa.2025.148235

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