We present SymFlux, a novel deep learning framework that performs symbolic regression to identify Hamiltonian functions from their corresponding vector fields on the standard symplectic plane. SymFlux models utilize hybrid CNN-LSTM architectures to learn and output the symbolic mathematical expression of the underlying Hamiltonian. Training and validation are conducted on newly developed datasets of Hamiltonian vector fields, a key contribution of this work. Our results demonstrate the model's effectiveness in accurately recovering these symbolic expressions, advancing automated discovery in Hamiltonian mechanics.
Cite
@article{arxiv.2507.06342,
title = {SymFlux: deep symbolic regression of Hamiltonian vector fields},
author = {M. A. Evangelista-Alvarado and P. Suárez-Serrato},
journal= {arXiv preprint arXiv:2507.06342},
year = {2025}
}