  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.
