Approximation of Nearly-Periodic Symplectic Maps via Structure-Preserving Neural Networks

Authors: Valentin Duruisseaux, Joshua W. Burby, and Qi Tang

This repository provides a simplified version of the Python/TensorFlow code used to generate some of the results in our paper

Approximation of Nearly-Periodic Symplectic Maps via Structure-Preserving Neural Networks.
Valentin Duruisseaux, Joshua W. Burby, and Qi Tang.
Scientific Reports, vol. 13, no. 8351, 2023.
Collection on "Physics-informed Machine Learning and its real-world applications"

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List of Files

The code is provided in two different formats

    NPMap_Learning.py     NPMap_Learning.ipynb

These codes contain detailed explanations with equations in LaTeX which are better rendered in the Jupyter notebook version.

The directory ./TrainingWeights/ contains the weights of the trained model whose results are presented in Figure 5 of our paper.

These weights can be loaded into the model by setting

    train = False

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Usage

    python ./NPMap_Learning.py

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Additional Information

This code is also published and available at https://www.osti.gov/biblio/1972078/

If you use this code in your research, please consider citing:

@article{Duruisseaux2023NPMap,
	author = {V. Duruisseaux, and J. W. Burby, and Q. Tang},
	title = {Approximation of nearly-periodic symplectic maps via structure-preserving neural networks},
	journal = {Scientific Reports, Collection on ``Physics-informed Machine Learning and its real-world applications"},
   	doi = {10.1038/s41598-023-34862-w},
	year = {2023}
}

@article{Duruisseaux2023NPMapCode,
	title = {Code Demonstration: Approximation of nearly-periodic symplectic maps via structure-preserving neural networks},
	author = {V. Duruisseaux, and J. W. Burby, and Q. Tang},
	doi = {10.2172/1972078},
	url = {https://www.osti.gov/biblio/1972078}, 
	year = {2023}
}

The software is available under the MIT License.