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

Area of Science:

• Fluid Dynamics
• Machine Learning
• Dynamical Systems

Background:

• Developing reduced-order models (ROMs) for chaotic fluid flows is crucial for efficient simulation and prediction.
• Traditional methods often struggle with the complexity and high dimensionality of turbulent and chaotic systems.

Purpose of the Study:

• To propose a novel machine learning framework for learning compact and interpretable ROMs for chaotic fluid flows.
• To enhance the predictive accuracy and efficiency of fluid flow models using deep learning techniques.

Main Methods:

• Utilized a β-variational autoencoder (β-VAE) to learn a compact latent representation of flow velocity data.
• Employed a transformer network to predict the temporal evolution of the learned latent-space dynamics.
• Tested the combined approach on numerical data from 2D viscous flows in both periodic and chaotic regimes.

Main Results:

• The β-VAE learned disentangled and interpretable latent features, similar to Proper Orthogonal Decomposition but more efficient.
• The transformer successfully predicted temporal dynamics in the latent space, capturing underlying flow behavior.
• Poincaré maps demonstrated that the proposed method accurately captures flow dynamics, outperforming existing prediction models.

Conclusions:

• The hybrid β-VAE and transformer approach provides an effective and interpretable method for ROMs of chaotic fluid flows.
• This technique offers significant potential for applications in weather forecasting, structural dynamics, and biomedical engineering.