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Disentangled Latent Spaces for Reduced Order Models using Deterministic Autoencoders

Henning Schwarz, Pyei Phyo Lin, Jens-Peter M. Zemke, Thomas Rung

TL;DR

This work compares deterministic autoencoders (OAE and UAE) with a β-VAE for disentangled latent spaces in data-driven reduced-order models of fluid dynamics. It demonstrates that the Uncorrelated Autoencoder (UAE) achieves robust reconstruction and low latent-variable correlations without probabilistic latents, outperforming β-VAE in several regimes and staying deterministic and easier to train. The study validates the approach on a 2D periodic flow benchmark and an industrial aircraft ditching loads dataset, showing that a small set of active latent variables suffices to capture key physics, even when the latent-space dimension is large. These results highlight UAE as a practical, interpretable surrogate modeling strategy for CFD applications, with clear pathways for mode generation and physics-aware latent-variable identification across tasks.

Abstract

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.

Disentangled Latent Spaces for Reduced Order Models using Deterministic Autoencoders

TL;DR

This work compares deterministic autoencoders (OAE and UAE) with a β-VAE for disentangled latent spaces in data-driven reduced-order models of fluid dynamics. It demonstrates that the Uncorrelated Autoencoder (UAE) achieves robust reconstruction and low latent-variable correlations without probabilistic latents, outperforming β-VAE in several regimes and staying deterministic and easier to train. The study validates the approach on a 2D periodic flow benchmark and an industrial aircraft ditching loads dataset, showing that a small set of active latent variables suffices to capture key physics, even when the latent-space dimension is large. These results highlight UAE as a practical, interpretable surrogate modeling strategy for CFD applications, with clear pathways for mode generation and physics-aware latent-variable identification across tasks.

Abstract

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 -variational autoencoders (-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 -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.

Paper Structure

This paper contains 21 sections, 4 equations, 26 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Orthogonal Autoencoder (OAE)
  4. Uncorrelated Autoencoder (UAE)
  5. Variational Autoencoder (VAE)
  6. Model Comparison
  7. Analysis of Latent Variables
  8. Mode Generation
  9. Results
  10. 2D Periodic Benchmark Flow
  11. Autoencoder Configuration
  12. Influence of Loss Function Weights
  13. Mode Analysis for Small Latent Space Dimension
  14. Physics Awareness for Higher Latent Space Dimension
  15. Pruning
  16. ...and 6 more sections

Figures (26)

  • Figure 1: Basic autoencoder scheme.
  • Figure 2: Scheme of a VAE.
  • Figure 3: Illustration of the 2D periodic flow configuration employed for the verification analysis solera-rico:2024Asztalos:2024solera_rico_2024_dataset.
  • Figure 4: Reconstruction errors obtained for the validation set and resulting absolute values of correlation coefficients between the two latent variables returned by the three different autoencoder models. The errorbars correspond to average, lowest and highest values obtained from five trainings.
  • Figure 5: True $u$- and $v$-velocity fields, model reconstructions and related errors for the exemplary reference snapshot of the verification case.
  • ...and 21 more figures