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