In fields where predictions may have vital consequences, uncertainty quantification (UQ) plays a crucial role, as it enables more accurate forecasts and mitigates the potential risks associated with decision-making. However, performing uncertainty quantification in real-world scenarios necessitates multiple evaluations of complex computational models, which can be both costly and time-consuming. To address these challenges, surrogate models (also known as meta-models)—which are low-cost approximations of computational models—can be an influential tool. Nonetheless, as the complexity of the problem increases and the number of input variables grows, the computational burden of constructing an efficient surrogate model also rises, leading to the so-called curse of dimensionality in uncertainty propagation from inputs to outputs. Additionally, dealing with constraints, ensuring the robustness and generalization of surrogate models across different inputs, and interpreting the output results can present significant difficulties. Therefore, techniques must be implemented to enhance the performance of these models. This paper reviews the developments of the past years in surrogate modeling for high-dimensional inputs, with the goal of quantifying output uncertainty. It proposes general approaches, including dimension reduction techniques, multi-fidelity surrogate models, and advanced sampling schemes, to overcome challenges in various practical problems. This comprehensive study provides an initial guide for effective surrogate modeling in engineering practices by outlining key components of solving algorithms and screening mathematical benchmark functions, all while ensuring sufficient accuracy for overall predictions. Additionally, this study identifies research gaps, suggests future directions, and describes the applications of the proposed solutions.

中文翻译：

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高维工程应用不确定性量化代理模型的最新进展综述


在预测可能产生重要后果的领域，不确定性量化 （UQ） 起着至关重要的作用，因为它能够实现更准确的预测并降低与决策相关的潜在风险。然而，在实际场景中执行不确定性量化需要对复杂的计算模型进行多次评估，这可能既昂贵又耗时。为了应对这些挑战，代理模型（也称为元模型）— 计算模型的低成本近似值 — 可以成为一种有影响力的工具。尽管如此，随着问题复杂性的增加和输入变量数量的增加，构建高效代理模型的计算负担也随之增加，从而导致从输入到输出的不确定性传播中所谓的维数诅咒。此外，处理约束、确保代理模型在不同输入中的稳健性和泛化性以及解释输出结果可能会带来重大困难。因此，必须实施技术来提高这些模型的性能。本文回顾了过去几年在高维输入代理建模方面的发展，目的是量化输出不确定性。它提出了通用方法，包括降维技术、多保真度代理模型和高级采样方案，以克服各种实际问题中的挑战。这项全面的研究通过概述求解算法的关键组成部分和筛选数学基准函数，为工程实践中的有效代理建模提供了初步指南，同时确保总体预测的足够准确性。 此外，本研究还确定了研究差距，提出了未来的方向，并描述了所提出解决方案的应用。