The code in this repository features a Python implementation of reduced-order model (ROM) of turbulent flow using $\beta$-variational autoencoders and transformer neural network. More details about the implementation and results from the training are available in "Towards optimal β-variational autoencoders combined with transformers for reduced-order modeling of turbulent flows", Yuning Wang, Alberto Solera-Rico, Carlos Sanmiguel Vila and Ricardo Vinuesa

We share the original data with 10,000 snapshots and 26,000 snapshots in OneDrive. We also provide the pre-trained models of $\beta$-VAE, transformers and LSTM in this repository. The obtined results such as temporal and spatial modes are available.

• To train $\beta$-VAE, please run:

    python beta_vae_train.py
  

• For post-processing, please run:

    python beta_vae_postprocess.py
  

• For ranking the $\beta$-VAE mode, please run:

    python beta_vae_rankModes.py
  

• To train a self-attention-based transformer, please run:

    python temporal_pred_train_selfattn.py
  

• For post-processing, pleas run:

    python temporal_pred_postprocess.py 
  

• To yield the sliding-window error $\epsilon$, please run:

    python temporal_pred_sliding_window.py 
  

• The transformer and LSTM archiectures are in the utils/NNs

• The $\beta$-VAE archiectures are in the utils/VAE

• The configurations of employed archiectures are in /utils/configs.py

We offer the scripts and data for reproducing the figures in the paper. For instance, to visualise the results of parametric studies, please run:

    python visual_lines.py

• 01_Data : The flow data of the streamwise velocity components of flow around square cylinder. Please find more details in the paper: "Causality analysis of large-scale structures in the flow around a wall-mounted square cylinder", Álvaro Martínez-Sánchez, Esteban López, Soledad Le Clainche, Adrián Lozano-Durán, Ankit Srivastava, Ricardo Vinuesa

• 02_Checkpoints : Store the $\beta$-VAE model, loss evolution and computation time in .pt format

• 03_Mode : Store the obtained $\beta$-VAE latent-space modes.

• 04_Figs : The figures and visualisation.

• 05_Pred : The data of temporal-dynamics predictions in latent space.

• 06_ROM : The time-series prediction for building the Reduce-order model (ROM)

• 07_Loss : The training loss evolution during training VAE.

• 08_POD : The results from Proper-orthogonal decomposition (POD)

• csvFile : The csv files to record $\beta$-VAE performance, where small denotes $Arch1$ and large denotes the $Arch2$, respectively.

• utils: The functions and architectures used in the scripts.