# Extending classical surrogate modelling to high-dimensions through supervised dimensionality reduction: a data-driven approach

arXiv: https://arxiv.org/abs/1812.06309 · HTML: https://mlsanity.com/paper/1812.06309/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Dec 2018.

## Built on by (most cited first, 16 of 16)

- [On the influence of over-parameterization in manifold based surrogates and deep neural operators](https://mlsanity.com/paper/2203.05071/) (2022)
- [A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems](https://mlsanity.com/paper/2202.04648/) (2022)
- [Learning in latent spaces improves the predictive accuracy of deep neural operators](https://mlsanity.com/paper/2304.07599/) (2023)
- [Manifold learning-based polynomial chaos expansions for high-dimensional surrogate models](https://mlsanity.com/paper/2107.09814/) (2021)
- [Active learning for structural reliability: survey, general framework and benchmark](https://mlsanity.com/paper/2106.01713/) (2021)
- [Polynomial Chaos Expansions on Principal Geodesic Grassmannian Submanifolds for Surrogate Modeling and Uncertainty Quantification](https://mlsanity.com/paper/2401.16683/) (2024)
- [Grassmannian diffusion maps based surrogate modeling via geometric harmonics](https://mlsanity.com/paper/2109.13805/) (2021)
- [PCENet: High Dimensional Surrogate Modeling for Learning Uncertainty](https://mlsanity.com/paper/2202.05063/) (2022)
- [Emulating the dynamics of complex systems using autoregressive models on manifolds (mNARX)](https://mlsanity.com/paper/2306.16335/) (2023)
- [All Emulators are Wrong, Many are Useful, and Some are More Useful Than Others: A Reproducible Comparison of Computer Model Surrogates](https://mlsanity.com/paper/2512.09060/) (2025)
- [Probabilistic partition of unity networks for high-dimensional regression problems](https://mlsanity.com/paper/2210.02694/) (2022)
- [Dimensionality reduction can be used as a surrogate model for high-dimensional forward uncertainty quantification](https://mlsanity.com/paper/2402.04582/) (2024)
- [Conditional deep generative models as surrogates for spatial field solution reconstruction with quantified uncertainty in Structural Health Monitoring applications](https://mlsanity.com/paper/2302.08329/) (2023)
- [Bayesian tomography using polynomial chaos expansion and deep generative networks](https://mlsanity.com/paper/2307.04228/) (2023)
- [Surrogate to Poincar'e inequalities on manifolds for dimension reduction in nonlinear feature spaces](https://mlsanity.com/paper/2505.01807/) (2025)
- [Non-intrusive surrogate modelling using sparse random features with applications in crashworthiness analysis](https://mlsanity.com/paper/2212.14507/) (2022)

## Abstract (arXiv)

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 O(102) 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 O(104)) 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.