This repository collects the Notebooks written for the numerical experiments of the paper: Paper on JCAM
The paper has been presented in a seminar here : Seminar
The Notebooks are divided into codes for Constrained and Unconstrained systems.
In the notebook Unconstrained_Hamiltonian_R4.ipynb we train a network to approximate a Hamiltonian having kinetic energy that couples the two components of the momentum.
In the notebook NoisyTrajectoriesRegularized.ipynb we test if training adding a regularization term that promotes the preservation of a known first integral allows to get better results for training sets with noisy trajectories.
In the notebook chainOfSphericalPendulums.ipynb we train a network to approximate the dynamcis of a chain of N connected spherical pendula. The number of connected pendula can be changed, and also four numerical integrators that can be adopted in the training are implemented.
In the notebook comparisonsParametersSection4.ipynb and the associated collected dataset of experiments CollectedData.csv there are the plots and tables for the parameter study reported in the paper. An alternative way to interact with the dataset is to go at the associated website Parameter study
To cite the paper use
@article{CELLEDONI2023114608, title = {Learning Hamiltonians of constrained mechanical systems}, journal = {Journal of Computational and Applied Mathematics}, volume = {417}, pages = {114608}, year = {2023}, issn = {0377-0427}, doi = {https://doi.org/10.1016/j.cam.2022.114608}, url = {https://www.sciencedirect.com/science/article/pii/S037704272200303X} }