  Variational autoencoder (VAE) architectures have the potential to develop
reduced-order models (ROMs) for chaotic fluid flows. We propose a method for
learning compact and near-orthogonal ROMs using a combination of a $\beta$-VAE
and a transformer, tested on numerical data from a two-dimensional viscous flow
in both periodic and chaotic regimes. The $\beta$-VAE is trained to learn a
compact latent representation of the flow velocity, and the transformer is
trained to predict the temporal dynamics in latent space. Using the $\beta$-VAE
to learn disentangled representations in latent-space, we obtain a more
interpretable flow model with features that resemble those observed in the
proper orthogonal decomposition, but with a more efficient representation.
Using Poincar\'e maps, the results show that our method can capture the
underlying dynamics of the flow outperforming other prediction models. The
proposed method has potential applications in other fields such as weather
forecasting, structural dynamics or biomedical engineering.

Fluid Dynamics;Machine Learning