Polynomial Chaos Expanded Gaussian Process

doi:10.3390/make8030078

2026-03-26

DOI：10.3390/make8030078

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摘要

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在复杂且未知的过程中，全局模型在整个输入域上进行拟合，但当响应曲面表现出非平稳行为和变化的光滑度时，往往表现不佳。一种常见的方法是使用局部模型，这需要将输入域划分为子域并训练多个模型，从而增加了显著的复杂性。认识到这一局限性，本研究旨在满足模型在全局域内一致表示输入-输出关系的同时，仍能适应响应的局部变化的需求。它引入了一种新颖的机器学习方法：多项式混沌展开高斯过程（PCEGP），利用多项式混沌展开计算高斯过程（GP）的输入依赖超参数。这种方法提供了一种具有数学可解释性的方法，通过纳入非平稳协方差函数和异方差噪声估计来生成局部自适应模型。该模型性能与不同算法在回归任务的基准测试中进行了比较。结果表明，PCEGP具有较低的预测误差，突显了其性能往往与以往方法相当或更优。所提出模型的一个关键优势在于其可解释的超参数，以及与标准GP相当的训练和预测运行时间。

Keyword:

machine learning

Gaussian process

polynomial chaos expansion

non-stationary covariance functions

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Machine Learning and Knowledge Extraction

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841

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university of duisburg essen

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university of applied sciences niederrhein

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