  Thanks to their versatility, ease of deployment and high-performance,
surrogate models have become staple tools in the arsenal of uncertainty
quantification (UQ). From local interpolants to global spectral decompositions,
surrogates are characterised by their ability to efficiently emulate complex
computational models based on a small set of model runs used for training. An
inherent limitation of many surrogate models is their susceptibility to the
curse of dimensionality, which traditionally limits their applicability to a
maximum of $\mathcal{O}(10^2)$ input dimensions. We present a novel approach at
high-dimensional surrogate modelling that is model-, dimensionality reduction-
and surrogate model- agnostic (black box), and can enable the solution of high
dimensional (i.e. up to $\mathcal{O}(10^4)$) problems. After introducing the
general algorithm, we demonstrate its performance by combining Kriging and
polynomial chaos expansions surrogates and kernel principal component analysis.
In particular, we compare the generalisation performance that the resulting
surrogates achieve to the classical sequential application of dimensionality
reduction followed by surrogate modelling on several benchmark applications,
comprising an analytical function and two engineering applications of
increasing dimensionality and complexity.
