# Active Subspaces in Infinite Dimension

arXiv: https://arxiv.org/abs/2510.11871 · HTML: https://mlsanity.com/paper/2510.11871/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 59 references that are in the map.
- First posted on arXiv 13 Oct 2025.

## Builds on (most cited first, 15 of 15)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Bayesian Optimization in a Billion Dimensions via Random Embeddings](https://mlsanity.com/paper/1301.1942/) (2013)
- [ANODE: Unconditionally Accurate Memory-Efficient Gradients for Neural ODEs](https://mlsanity.com/paper/1902.10298/) (2019)
- [A survey on high-dimensional Gaussian process modeling with application to Bayesian optimization](https://mlsanity.com/paper/2111.05040/) (2021)
- [Large-scale Bayesian optimal experimental design with derivative-informed projected neural network](https://mlsanity.com/paper/2201.07925/) (2022)
- [Sequential Learning of Active Subspaces](https://mlsanity.com/paper/1907.11572/) (2019)
- [Deep active subspaces - a scalable method for high-dimensional uncertainty propagation](https://mlsanity.com/paper/1902.10527/) (2019)
- [Sensitivity analysis for multidimensional and functional outputs](https://mlsanity.com/paper/1311.1797/) (2013)
- [Sensitivity Prewarping for Local Surrogate Modeling](https://mlsanity.com/paper/2101.06296/) (2021)
- [Co-Active Subspace Methods for the Joint Analysis of Adjacent Computer Models](https://mlsanity.com/paper/2311.18146/) (2023)
- [Bayesian functional optimisation with shape prior](https://mlsanity.com/paper/1809.07260/) (2018)
- [Sequential Subspace Search for Functional Bayesian Optimization Incorporating Experimenter Intuition](https://mlsanity.com/paper/2009.03543/) (2020)
- [Discovering Active Subspaces for High-Dimensional Computer Models](https://mlsanity.com/paper/2307.11241/) (2023)
- [Non-commutative Discretize-then-Optimize Algorithms for Elliptic PDE-Constrained Optimal Control Problems](https://mlsanity.com/paper/1706.07652/) (2017)
- [Shared active subspace for multivariate vector-valued functions](https://mlsanity.com/paper/2401.02735/) (2024)

## Built on by (most cited first, 1 of 1)

- [Bayesian Optimization on Function Spaces via Sparse RKHS Manifolds](https://mlsanity.com/paper/2610.07417/) (2026)

## Abstract (arXiv)

Active subspace analysis uses the leading eigenspace of the gradient's second moment to conduct supervised dimension reduction. In this article, we extend this methodology to real-valued functionals on Hilbert space. We define an operator which coincides with the active subspace matrix when applied to a Euclidean space. We show that many of the desirable properties of Active Subspace analysis extend directly to the infinite dimensional setting. We also propose a Monte Carlo procedure and discuss its convergence properties. Finally, we deploy this methodology to create visualizations and improve modeling and optimization on complex test problems.