Thanks to their versatility, ease of deployment and high-performance, surrogate models have become staple tools in the arsenal of uncertainty quantification (UQ). From local interpolants to global spectral decompositions, surrogates are characterised by their ability to efficiently emulate complex computational models based on a small set of model runs used for training. An inherent limitation of many surrogate models is their susceptibility to the curse of dimensionality, which traditionally limits their applicability to a maximum of $\mathcal{O}(10^2)$ input dimensions. We present a novel approach at high-dimensional surrogate modelling that is model-, dimensionality reduction- and surrogate model- agnostic (black box), and can enable the solution of high dimensional (i.e. up to $\mathcal{O}(10^4)$) problems. After introducing the general algorithm, we demonstrate its performance by combining Kriging and polynomial chaos expansions surrogates and kernel principal component analysis. In particular, we compare the generalisation performance that the resulting surrogates achieve to the classical sequential application of dimensionality reduction followed by surrogate modelling on several benchmark applications, comprising an analytical function and two engineering applications of increasing dimensionality and complexity.

中文翻译：

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通过监督降维将经典代理建模扩展到高维：一种数据驱动的方法

由于其多功能性、易于部署和高性能，替代模型已成为不确定性量化 (UQ) 库中的主要工具。从局部插值到全局谱分解，代理的特点是它们能够基于用于训练的一小组模型运行有效地模拟复杂的计算模型。许多代理模型的一个固有限制是它们对维度灾难的敏感性，这传统上将它们的适用性限制为最大 $\mathcal{O}(10^2)$ 输入维度。我们在高维代理建模中提出了一种新方法，即模型、降维和代理模型不可知（黑盒），并且可以实现高维的解决方案（即高达 $\mathcal{O}(10^ 4)$) 问题。在介绍了通用算法之后，我们通过结合克里金法和多项式混沌展开代理以及核主成分分析来证明其性能。特别是，我们将生成的代理实现的泛化性能与降维的经典顺序应用程序进行比较，然后在几个基准应用程序上进行代理建模，包括一个分析函数和两个增加维度和复杂性的工程应用程序。