# Disentangled Latent Spaces for Reduced Order Models using Deterministic Autoencoders

arXiv: https://arxiv.org/abs/2502.14679 · HTML: https://mlsanity.com/paper/2502.14679/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 39 references that are in the map.
- First posted on arXiv 20 Feb 2025.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [β-Variational autoencoders and transformers for reduced-order modelling of fluid flows](https://mlsanity.com/paper/2304.03571/) (2023)
- [Measuring Disentanglement: A Review of Metrics](https://mlsanity.com/paper/2012.09276/) (2020)
- [Towards extraction of orthogonal and parsimonious non-linear modes from turbulent flows](https://mlsanity.com/paper/2109.01514/) (2021)
- [Deep Neural Networks for Nonlinear Model Order Reduction of Unsteady Flows](https://mlsanity.com/paper/2007.00936/) (2020)
- [Physics-aware Reduced-order Modeling of Transonic Flow via β-Variational Autoencoder](https://mlsanity.com/paper/2205.00608/) (2022)
- [Be More Active! Understanding the Differences between Mean and Sampled Representations of Variational Autoencoders](https://mlsanity.com/paper/2109.12679/) (2021)
- [Disentangling Generative Factors of Physical Fields Using Variational Autoencoders](https://mlsanity.com/paper/2109.07399/) (2021)
- [Uncorrelated Feature Encoding for Faster Image Style Transfer](https://mlsanity.com/paper/1807.01493/) (2018)
- [Machine Learning based Prediction of Ditching Loads](https://mlsanity.com/paper/2402.10724/) (2024)

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

- [Conditional Neural Field based Reduced Order Model for Dynamic Ditching Load Prediction](https://mlsanity.com/paper/2605.21499/) (2026)
- [Learning Control-Affine Reduced-Order Models via Autoencoders](https://mlsanity.com/paper/2606.05045/) (2026)

## Abstract (arXiv)

Data-driven reduced-order models based on autoencoders generally lack interpretability compared to classical methods such as the proper orthogonal decomposition. More interpretability can be gained by disentangling the latent variables and analyzing the resulting modes. For this purpose, probabilistic β-variational autoencoders (β-VAEs) are frequently used in computational fluid dynamics and other simulation sciences. Using a benchmark periodic flow dataset, we show that competitive results can be achieved using non-probabilistic autoencoder approaches that either promote orthogonality or penalize correlation between latent variables. Compared to probabilistic autoencoders, these approaches offer more robustness with respect to the choice of hyperparameters entering the loss function. We further demonstrate the ability of a non-probabilistic approach to identify a reduced number of active latent variables by introducing a correlation penalty, a function also known from the use of β-VAE. The investigated probabilistic and non-probabilistic autoencoder models are finally used for the dimensionality reduction of aircraft ditching loads, which serves as an industrial application in this work.