# Deep active subspaces - a scalable method for high-dimensional uncertainty propagation

arXiv: https://arxiv.org/abs/1902.10527 · HTML: https://mlsanity.com/paper/1902.10527/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2019.

## Built on by (most cited first, 7 of 7)

- [Learning Active Subspaces for Effective and Scalable Uncertainty Quantification in Deep Neural Networks](https://mlsanity.com/paper/2309.03061/) (2023)
- [Surrogate assisted active subspace and active subspace assisted surrogate -- A new paradigm for high dimensional structural reliability analysis](https://mlsanity.com/paper/2105.04979/) (2021)
- [Accelerating Hamiltonian Monte Carlo for Bayesian Inference in Neural Networks and Neural Operators](https://mlsanity.com/paper/2507.14652/) (2025)
- [Active Subspaces in Infinite Dimension](https://mlsanity.com/paper/2510.11871/) (2025)
- [RMFGP: Rotated Multi-fidelity Gaussian process with Dimension Reduction for High-dimensional Uncertainty Quantification](https://mlsanity.com/paper/2204.04819/) (2022)
- [Regression Trees Know Calculus](https://mlsanity.com/paper/2405.13846/) (2024)
- [Structured Neural Chaos: An Adaptive Surrogate Modeling Framework for Functional Uncertainty Quantification and Global Sensitivity Analysis](https://mlsanity.com/paper/2607.28903/) (2026)

## Abstract (arXiv)

A problem of considerable importance within the field of uncertainty quantification (UQ) is the development of efficient methods for the construction of accurate surrogate models. Such efforts are particularly important to applications constrained by high-dimensional uncertain parameter spaces. The difficulty of accurate surrogate modeling in such systems, is further compounded by data scarcity brought about by the large cost of forward model evaluations. Traditional response surface techniques, such as Gaussian process regression (or Kriging) and polynomial chaos are difficult to scale to high dimensions. To make surrogate modeling tractable in expensive high-dimensional systems, one must resort to dimensionality reduction of the stochastic parameter space. A recent dimensionality reduction technique that has shown great promise is the method of `active subspaces'. The classical formulation of active subspaces, unfortunately, requires gradient information from the forward model - often impossible to obtain. In this work, we present a simple, scalable method for recovering active subspaces in high-dimensional stochastic systems, without gradient-information that relies on a reparameterization of the orthogonal active subspace projection matrix, and couple this formulation with deep neural networks. We demonstrate our approach on synthetic and real world datasets and show favorable predictive comparison to classical active subspaces.