Scattering Dynamics with WSINDy

Python code accompanying the manuscript "Learning effective soliton dynamics from scattering data," submitted to the Journal of Nonlinear Waves.

@misc{minor2026learningeffectivesolitondynamics,
      title={Learning Effective Soliton Dynamics from Scattering Data}, 
      author={Seth Minor and Vanja Dukic and David M. Bortz},
      year={2026},
      eprint={2607.01545},
      archivePrefix={arXiv},
      primaryClass={physics.comp-ph},
      url={https://arxiv.org/abs/2607.01545}, 
}

Also see:

• Zenodo: coming soon...
• ArXiV pre-print: https://doi.org/10.48550/arXiv.2607.01545
• To recreate results in the paper, see recreate_paper_results.ipynb and recreate_figures.ipynb.
• The tutorials and examples located here for instructions on how to use the wsindy_ode.

We use experimental data taken from a study by Heinrich et al. (2026):

@data{MRTNPI_2026,
      author = {Kjell Søren Heinrich and Svensson Seth, Douglas and Ehrnstrom, Mats and Ellingsen, Simen Ådnøy},
      publisher = {DataverseNO},
      title = {{Replication Data for: Rediscovering shallow-water equations from experimental data}},
      year = {2026},
      version = {V1},
      doi = {10.18710/MRTNPI},
      url = {https://doi.org/10.18710/MRTNPI}
}

This algorithm uses the following dependencies:

torch
scipy
numpy
itertools
symengine
tqdm

Install WSINDy in a Bash environment:

wget -q https://raw.githubusercontent.com/SethMinor/PyWSINDy-for-PDEs/main/wsindy.py
wget -q https://raw.githubusercontent.com/SethMinor/PyWSINDy-for-PDEs/main/wsindy_ode.py
wget -q https://raw.githubusercontent.com/SethMinor/PyWSINDy-for-PDEs/main/helper_fcns.py