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.

本文提出了一种使用beta-VAE和transformer联合学习载于流体速度和时间动态的短小且近似正交的约简模型，可用于流体力学、气象预测、结构动力学或生物医学工程等其他领域的建模分析。

$β$-变分自编码器和Transformer用于流体流动的降阶建模