Latent Dynamics Networks

This repository contains codes accompanying the paper [1], introducing Latent Dynamics Network (LDNets), a scientific machine learning method capable of uncovering low-dimensional intrinsic dynamics in systems exhibiting a spatio-temporal behavior in response to external stimuli. LDNets automatically discover a low-dimensional manifold while learning the system dynamics, eliminating the need for training an auto-encoder and avoiding operations in the high-dimensional space. They predict the evolution, even in time-extrapolation scenarios, of space-dependent fields without relying on predetermined grids, thus enabling weight-sharing across query-points. Lightweight and easy-to-train, LDNets demonstrate superior accuracy (normalized error 5 times smaller) in highly-nonlinear problems, with significantly fewer trainable parameters (more than 10 times fewer) compared to state-of-the-art methods.

Requirements

To run these codes, you need Python (version 3.9) with the modules listed in the file requirements.txt. If you are using pip, you can install them by running:

pip install -r requirements.txt

Downloading data

To replicate the results presented in the paper [1], the necessary training and testing data have been organized in a dedicated Zenodo repository. Follow the steps below to incorporate the data into your local repository:

1. Navigate to this Zenodo repository.

2. Download the data.zip file from the repository.

3. Extract the contents of data.zip to the root level of your local copy of this repository. This will generate a new folder named data.

You can also achieve this by running this script:

curl https://zenodo.org/records/10436827/files/data.zip -o data.zip
unzip data.zip -d data
rm data.zip

References

[1] F. Regazzoni, S. Pagani, M. Salvador, L. Dede', A. Quarteroni, "Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks" Nature Communications (2024) 15, 1834