Learning Partial Differential Equations in Emergent Coordinates

This package builds upon the lpde python package (see this GitHub repo) to learn partial differential equations in emergent coordinates.

USAGE

Via source

git clone https://github.com/fkemeth/emergent_pdes
cd emergent_pdes/
pip install -r requirements.txt

This repository contains five different examples:

• cgle_periodic: Contains code to learn a partial differental equation describing the periodic dynamics in the complex Ginzburg-Landau equation.
• cgle_chaotic: Contains code to learn a partial differental equation describing the chaotic dynamics in the complex Ginzburg-Landau equation.
• sle_periodic: Contains code to learn a partial differental equation describing the periodic dynamics in an ensemble of Stuart-Landau oscillators.
• sle_gamma: Contains code to learn a partial differental equation describing the dynamics in an ensemble of Stuart-Landau oscillators for different parameter values.
• preboetzinger: Contains code to learn a partial differential equation describing the periodic dynamics of a biologically-motivated system of coupled neurons.

Each example can be run using

python run.py

in the respective example folders.

• Configuration files are contained in the config/ subdirectories.
• Some examples contain testing scripts in tests.py

NOTE

This work is under constant development and might undergo significant changes in the future!

ISSUES

For questions, please contact (felix@kemeth.de), or visit the GitHub repo.

LICENCE

This work is licenced under MIT License. Please cite

"Learning emergent partial differential equations in a learned emergent space" F.P. Kemeth et al. Nature Communications 13, Article number: 3318 (2022) (https://www.nature.com/articles/s41467-022-30628-6)

if you use this package for publications.