# Neural active manifolds: nonlinear dimensionality reduction for uncertainty quantification

arXiv: https://arxiv.org/abs/2408.03534 · HTML: https://mlsanity.com/paper/2408.03534/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 50 references that are in the map.
- First posted on arXiv 7 Aug 2024.

## Builds on (most cited first, 5 of 5)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems](https://mlsanity.com/paper/2202.04648/) (2022)
- [Active Manifolds: A non-linear analogue to Active Subspaces](https://mlsanity.com/paper/1904.13386/) (2019)
- [A comprehensive and biophysically detailed computational model of the whole human heart electromechanics](https://mlsanity.com/paper/2207.12460/) (2022)
- [Improved multifidelity Monte Carlo estimators based on normalizing flows and dimensionality reduction techniques](https://mlsanity.com/paper/2312.12361/) (2023)

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

- [Enabling stratified sampling in high dimensions via nonlinear dimensionality reduction](https://mlsanity.com/paper/2506.08921/) (2025)
- [On the performance of multi-fidelity and reduced-dimensional neural emulators for inference of physiological boundary conditions](https://mlsanity.com/paper/2506.11683/) (2025)

## Abstract (arXiv)

We present a new approach for nonlinear dimensionality reduction, specifically designed for computationally expensive mathematical models. We leverage autoencoders to discover a one-dimensional neural active manifold (NeurAM) capturing the model output variability, through the aid of a simultaneously learnt surrogate model with inputs on this manifold. Our method only relies on model evaluations and does not require the knowledge of gradients. The proposed dimensionality reduction framework can then be applied to assist outer loop many-query tasks in scientific computing, like sensitivity analysis and multifidelity uncertainty propagation. In particular, we prove, both theoretically under idealized conditions, and numerically in challenging test cases, how NeurAM can be used to obtain multifidelity sampling estimators with reduced variance by sampling the models on the discovered low-dimensional and shared manifold among models. Several numerical examples illustrate the main features of the proposed dimensionality reduction strategy and highlight its advantages with respect to existing approaches in the literature.