β-Variational autoencoders and transformers for reduced-order modelling of fluid flows.

Variational autoencoder architectures have the potential to develop reduced-order models for chaotic fluid flows. We propose a method for learning compact and near-orthogonal reduced-order models using a combination of a β-variational autoencoder and a transformer, tested on numerical data from a two-dimensional viscous flow in both periodic and chaotic regimes. The β-variational autoencoder 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.