Symplectic ROM — Numerical Experiments

About the Paper

This code accompanies our paper “Reduced-order modeling of Hamiltonian dynamics based on symplectic neural networks.”
The work proposes a symplectic reduced-order modeling framework that unifies latent-space discovery and latent dynamics via HenonNets (with optional linear symplectic layers), yielding an exact symplectic map and long-horizon stability; we validate the approach on canonical Hamiltonian systems.

This repository contains code for three numerical experiment suites:

• linear/ — 1D linear wave equation
• param/ — Parametric linear wave equation
• schro/ — 1D nonlinear Schrödinger (NLS) equation

Each folder contains two Jupyter notebooks:

1. *_data_generation.ipynb: Run this first to generate the simulation data.
2. symp_*.ipynb: Run this second to build, train, and test the symplectic reduced-order model.

Environment Setup

The code requires:

• Python ≥ 3.10
• JupyterLab or Jupyter Notebook
• NumPy, SciPy, Matplotlib, Pandas
• TensorFlow ≥ 2.12

A quick setup using conda is recommended:

conda create -n symprom python=3.11 -y
conda activate symprom
pip install numpy scipy matplotlib pandas jupyterlab tensorflow

How to Run

The procedure is the same for all examples. Using the linear/ experiment as an example:

1. Generate Data: Open and run all cells in linear/linear_data_generation.ipynb. This will generate data/features.npy (and labels.npy; a test.npy may be optionally created).
2. Train and Test Model: Open and run all cells in linear/symp_linear_wave.ipynb.

The param/ and schro/ folders follow the identical procedure.

Reproducibility

Each notebook sets random seeds at the beginning for reproducibility. Please keep the default seed values or change them explicitly if needed.

Data Size

The full datasets used in the paper may be large. This repository includes smaller sample datasets to allow for quick verification and reproduction of the code. Instructions for generating full datasets or links to download them are provided in the respective data generation notebooks.

Citation

If you use this repository or build upon our method, please cite:

Chen, Y., Guo, W., Tang, Q., & Zhong, X. Reduced-order modeling of Hamiltonian dynamics based on symplectic neural networks. arXiv:2508.11911, 2025. DOI: 10.48550/arXiv.2508.11911.

BibTeX

@misc{chen2025reducedordermodelinghamiltoniandynamics,
      title={Reduced-order modeling of Hamiltonian dynamics based on symplectic neural networks}, 
      author={Yongsheng Chen and Wei Guo and Qi Tang and Xinghui Zhong},
      year={2025},
      eprint={2508.11911},
      archivePrefix={arXiv},
      primaryClass={math.NA},
      url={https://arxiv.org/abs/2508.11911}, 
}