SymFlux is a novel deep learning framework for symbolic regression that identifies Hamiltonian functions from their corresponding vector fields on the standard symplectic plane. SymFlux models use a hybrid CNN-LSTM architecture to learn and output the symbolic mathematical expression of the underlying Hamiltonian.
This repository accompanies our paper 'SymFlux: deep symbolic regression of Hamiltonian vector fields'.
This article is motivated by the following articles:
-
O. Vinyals, A. Toshev, S. Bengio & D. Erhan,
Show and tell: A neural image caption generator,
Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 3156–3164 (2015). -
M. A. Evangelista-Alvarado, J. C. Ruíz-Pantaleón & P. Suárez-Serrato,
On computational Poisson geometry I: Symbolic foundations,
Journal of Geometric Mechanics 13(4), 607–628 (2021). -
M. A. Evangelista-Alvarado, José Crispín Ruíz-Pantaleón & P. Suárez-Serrato,
On computational Poisson geometry II: Numerical methods,
Journal of Computational Dynamics 8(3), 273–307 (2021).
Our issue tracker is at https://github.com/appliedgeometry/symflux/issues. Please report any bugs that you find. Or, even better, if you are interested in our project you can fork the repository on GitHub and create a pull request.
MIT licence
This work is developed and maintained by:
- M. A. Evangelista Alvarado - @mevangelista-alvarado
- P. Suárez Serrato - @psuarezserrato
@misc{symflux2025,
title={SymFlux: deep symbolic regression of Hamiltonian vector fields},
author={M. A. Evangelista-Alvarado and P. Suárez-Serrato},
year={2025},
eprint={2507.06342},
archivePrefix={arXiv},
primaryClass={cs.LG},
url={https://arxiv.org/abs/2507.06342},
}
The authors thank DGTIC-UNAM for using the Miztli supercomputer HPC resources, to train and experiment on the deep learning models in this work through the grant LANCAD-UNAM-DGTIC-430. MAEA wishes to also thank CONACyT for a doctoral fellowship held during the production of this work.