Predictive estimation, which comprises model calibration, model prediction, and validation, is a common objective when performing inverse uncertainty quantification (UQ) in diverse scientific applications. These techniques typically require thousands to millions of realisations of the forward model, leading to high computational costs. Surrogate models are often used to approximate these simulations. However, many surrogate models suffer from the fundamental limitation of being unable to estimate plausible high-dimensional outputs, inevitably compromising their use in the UQ framework. To address this challenge, this study introduces an efficient surrogate modelling workflow tailored for high-dimensional outputs. Specifically, a two-step approach is developed: (1) a dimensionality reduction technique is used for extracting data features and mapping the original output space into a reduced space; and (2) a multivariate surrogate model is constructed directly on the reduced space. The combined approach is shown to improve the accuracy of the surrogate model while retaining the computational efficiency required for UQ inversion. The proposed surrogate method, combined with Bayesian inference, is evaluated for a civil engineering application by performing inverse analyses on a laterally loaded pile problem. The results demonstrate the superiority of the proposed framework over traditional surrogate methods in dealing with high-dimensional outputs for sequential inversion analysis.

翻译：预测性估计（包含模型校准、模型预测与验证）是各类科学应用中进行反演不确定性量化时的常见目标。此类技术通常需要数千至数百万次正演模型实现，导致计算成本高昂。代理模型常被用于近似这些模拟。然而，许多代理模型存在根本性局限：无法估计合理的高维输出，这必然影响其在不确定性量化框架中的应用。为应对这一挑战，本研究提出一种针对高维输出量身定制的高效代理建模工作流程。具体而言，开发了一种两步法：（1）采用降维技术提取数据特征，并将原始输出空间映射至降维空间；（2）直接在降维空间上构建多元代理模型。该组合方法在保持反演不确定性量化所需计算效率的同时，提高了代理模型的精度。通过将所提出的代理方法与贝叶斯推断相结合，并针对侧向受荷桩基问题进行反演分析，在一个土木工程应用中对该方法进行了评估。结果表明，在处理序列反演分析中的高维输出时，所提出的框架优于传统代理方法。