A two-step surrogate method for sequential uncertainty quantification in high-dimensional inverse problems

TL;DR

The paper tackles the computational burden of inverse uncertainty quantification with high-dimensional outputs by introducing a two-step DR-based surrogate that couples PCA for output dimensionality reduction with a multivariate PCE surrogate. This PCA-PCE framework enables Bayesian inversion to operate in a reduced space while preserving output covariance, yielding significant gains in efficiency and accuracy for high-dimensional problems. Demonstrated on a civil/geotechnical problem involving a laterally loaded pile in glacial clay, the method outperforms traditional per-QoI surrogates, particularly when training data are scarce, and supports sequential data assimilation through Bayesian updating. The work provides a practical, scalable pathway for rapid, predictive UQ in complex, high-dimensional forward models with direct applicability to offshore wind turbine and foundation engineering problems.

Abstract

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.

Figures (11)

• Figure 2.1: A visualised PCA process
• Figure 2.2: DR-flowchart
• Figure 2.3: A two-step surrogate model construction: PCA-PCE
• Figure 3.1: Sequential Bayesian inversion
• Figure 3.2: PCA-PCE surrogate in Bayesian inversion