# Dimensionality reduction can be used as a surrogate model for high-dimensional forward uncertainty quantification

arXiv: https://arxiv.org/abs/2402.04582 · HTML: https://mlsanity.com/paper/2402.04582/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 66 references that are in the map.
- First posted on arXiv 7 Feb 2024.

## Builds on (most cited first, 17 of 17)

- [Language Modeling Is Compression](https://mlsanity.com/paper/2309.10668/) (2023)
- [Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantification](https://mlsanity.com/paper/1802.00850/) (2018)
- [On the influence of over-parameterization in manifold based surrogates and deep neural operators](https://mlsanity.com/paper/2203.05071/) (2022)
- [Heterogeneous Multi-output Gaussian Process Prediction](https://mlsanity.com/paper/1805.07633/) (2018)
- [A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems](https://mlsanity.com/paper/2202.04648/) (2022)
- [Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems](https://mlsanity.com/paper/1901.04878/) (2019)
- [Extending classical surrogate modelling to high-dimensions through supervised dimensionality reduction: a data-driven approach](https://mlsanity.com/paper/1812.06309/) (2018)
- [Manifold learning-based polynomial chaos expansions for high-dimensional surrogate models](https://mlsanity.com/paper/2107.09814/) (2021)
- [An active-learning algorithm that combines sparse polynomial chaos expansions and bootstrap for structural reliability analysis](https://mlsanity.com/paper/1709.01589/) (2017)
- [Emulation of stochastic simulators using generalized lambda models](https://mlsanity.com/paper/2007.00996/) (2020)
- [Stochastic spectral embedding](https://mlsanity.com/paper/2004.04480/) (2020)
- [Grassmannian diffusion maps based dimension reduction and classification for high-dimensional data](https://mlsanity.com/paper/2009.07547/) (2020)
- [Entropy-based closure for probabilistic learning on manifolds](https://mlsanity.com/paper/1803.08161/) (2018)
- [Bayesian model inversion using stochastic spectral embedding](https://mlsanity.com/paper/2005.07380/) (2020)
- [Uncertainty propagation of p-boxes using sparse polynomial chaos expansions](https://mlsanity.com/paper/1608.05565/) (2016)
- [Probabilistic Performance-Pattern Decomposition (PPPD): analysis framework and applications to stochastic mechanical systems](https://mlsanity.com/paper/2003.02205/) (2020)
- [Optimized Equivalent Linearization for Random Vibration](https://mlsanity.com/paper/2208.08991/) (2022)

## Built on by (most cited first, 2 of 2)

- [Constructing balanced datasets for predicting failure modes in structural systems under seismic hazards](https://mlsanity.com/paper/2503.01882/) (2025)
- [Probabilistic function-on-function nonlinear autoregressive model for emulation and reliability analysis of stochastic dynamical systems](https://mlsanity.com/paper/2602.01929/) (2026)

## Abstract (arXiv)

We introduce a method to construct a stochastic surrogate model from the results of dimensionality reduction in forward uncertainty quantification. The hypothesis is that the high-dimensional input augmented by the output of a computational model admits a low-dimensional representation. This assumption can be met by numerous uncertainty quantification applications with physics-based computational models. The proposed approach differs from a sequential application of dimensionality reduction followed by surrogate modeling, as we "extract" a surrogate model from the results of dimensionality reduction in the input-output space. This feature becomes desirable when the input space is genuinely high-dimensional. The proposed method also diverges from the Probabilistic Learning on Manifold, as a reconstruction mapping from the feature space to the input-output space is circumvented. The final product of the proposed method is a stochastic simulator that propagates a deterministic input into a stochastic output, preserving the convenience of a sequential "dimensionality reduction + Gaussian process regression" approach while overcoming some of its limitations. The proposed method is demonstrated through two uncertainty quantification problems characterized by high-dimensional input uncertainties.