Multiscale Simulations of Complex Systems by Learning their Effective Dynamics

Code and data for the paper: PR Vlachas, G. Arampatzis, C. Uhler, and P Koumoutsakos, Multiscale Simulations of Complex Systems by Learning their Effective Dynamics, Nature Machine Intelligence, 2022.

Demonstration on the FitzHugh Nagumo Equation (FHN)

The scripts to generate the training, validation, and test data for each application can be found in the ./Data folder. Run these scripts in the respective order, i.e. for the FHN equation:

python3 0_data_gen.py
python3 1_creating_figures.py
python3 2_create_training_data.py
python3 3_data_gen_test.py
python3 4_create_test_data.py

In case you cannot generate the data, please raise an issue. The data for the FHN equation can be also found online here. Download the compressed file, uncompress it, and lace the uncompressed folders/files in the directory ./Data/FHN/Data/.

Once the data are generated, navigate to ./Code/Experiments/FHN/Local and run any of the scripts.

Script	Description
0_PCA.sh	Training and testing the dimensionality reduction with PCA/DiffMaps.
1_PCA_RC.sh	Training and testing a Reservoir Computer with PCA/DiffMaps on the latent space (and multiscale testing)
2_PCA_SINDy.sh	PCA/DiffMaps + SINDy
3_PCA_RNN.sh	PCA/DiffMaps + RNN (LSTM/GRU)
4_AE.sh	Training a Convolutional Autoencoder (CNN)
5_AE_RNN.sh	LED (CNN+LSTM)
5_AE_RC.sh	LED (AE+RC)

These scripts train and test the respective networks or dimensionality reduction methods, and generate plots and files with diagnostics in the ./Results folder.

Data availability

• Scripts to generate the data for the FHN and the KS equations are provided in the ./Data folder.
• In addition, the data for the FHN equation are shared here.
• Data for the Navier-Stokes flow past a cylinder have been generated using the in-house software library, CubismUP-2D / Cubism-AMR.

Environment Setup

To set up the python environment the poetry dependency manager is used. The dependencies are described in the pyproject.toml file. To set up the environment:

1. Enter the project's root directory.
2. Open a new shell, and create / activate the environment.

poetry shell

3. Install all module dependencies including development,

poetry install