Extending classical surrogate modelling to high-dimensions through supervised dimensionality reduction: a data-driven approach
This addresses a scalability problem for uncertainty quantification practitioners, offering an incremental advance by extending existing methods to higher dimensions.
The paper tackles the curse of dimensionality in surrogate models, which traditionally limits them to about 100 input dimensions, by introducing a novel black-box approach that enables handling up to 10,000 dimensions, as demonstrated with improved generalization performance on benchmark applications.
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.