Advection-aware autoencoders and long-short-term memory networks for reduced order modeling of parametric, advection-dominated PDEs

This is supporting code for the article

Dutta, S.; Rivera-Casillas, P.; Styles, B.; Farthing, M.W.
Reduced Order Modeling Using Advection-Aware Autoencoders.
Math. Comput. Appl. 2022, 27, 34. https://doi.org/10.3390/mca27030034

This article is part of the Special Issue: "Computational Methods for Coupled Problems in Science and Engineering".

Email: sourav.dutta@erdc.dren.mil for any questions/feedback.

Advection-aware Autoencoder Architecture

Getting Started

• Generate the high-fidelity snapshot data for the 2D linear advection example by running the script examples/2DLinearAdvection.py. It automatically saves the snapshot files in the data directory.
• Generate the high-fidelity snapshot data for the 1D Burgers example by running the notebook examples/1DBurgers_data.ipynb. It automatically saves the snapshot files in the data directory and generates snapshot visualizations.

Dependencies

• Python 3.x
• Tensorflow TF 2.x. Install either the CPU or the GPU version depending on available resources.
• A list of all the dependencies are provided in the requirements file.

Executing program

• The AA autoencoder training and evaluation can be performed using the notebooks examples/AA_autoencoder_parametric_2DLinearAdvection.ipynb and examples/AA_autoencoder_parametric_1DBurgers.ipynb.
• The performance of the various AA autoencoder models are compared in the notebooks examples/AA_autoencoder_comparison_2DLinearAdvection.ipynb and examples/AA_autoencoder_comparison_1DBurgers.ipynb.
• The LSTM and parametric LSTM models for the 1D Burgers' example are trained and evaluated using the notebooks examples/LSTM_1DBurgers.ipynb and examples/pLSTM_parametric_1DBurgers.ipynb.