标题： 从高斯过程采样：教程及在全局敏感性分析和优化中的应用 显示英文标题

标题： Sampling from Gaussian Processes: A Tutorial and Applications in Global Sensitivity Analysis and Optimization

摘要： 高保真度的模拟和物理实验对于工程分析和设计至关重要。 然而，它们的高成本通常限制了它们在两个关键任务中的应用：全局敏感性分析（GSA）和优化。 这一限制促使了高斯过程（GPs）作为代理回归模型的常用方法，以基于有限数量的高质量观测值提供具有不确定性的预测。 GPs自然地支持高效的采样策略，通过从感兴趣模型的可能函数子集提取信息，从而在不确定性下做出明智的决策。 尽管在机器学习和统计学界很受欢迎，但从GPs中进行采样在工程优化领域却很少受到关注。 在本文中，我们提出了两种显著的采样方法——随机傅里叶特征和路径条件——的公式和详细实现，用于从GPs生成后验样本。 其他方法简要描述。 重要的是，我们详细说明了生成的样本如何应用于GSA、单目标优化和多目标优化。 我们通过一系列数值例子展示了这些采样方法的成功应用。 显示英文摘要

摘要： High-fidelity simulations and physical experiments are essential for engineering analysis and design. However, their high cost often limits their applications in two critical tasks: global sensitivity analysis (GSA) and optimization. This limitation motivates the common use of Gaussian processes (GPs) as proxy regression models to provide uncertainty-aware predictions based on a limited number of high-quality observations. GPs naturally enable efficient sampling strategies that support informed decision-making under uncertainty by extracting information from a subset of possible functions for the model of interest. Despite their popularity in machine learning and statistics communities, sampling from GPs has received little attention in the community of engineering optimization. In this paper, we present the formulation and detailed implementation of two notable sampling methods -- random Fourier features and pathwise conditioning -- for generating posterior samples from GPs. Alternative approaches are briefly described. Importantly, we detail how the generated samples can be applied in GSA, single-objective optimization, and multi-objective optimization. We show successful applications of these sampling methods through a series of numerical examples.