Improving Long-Range Interactions in Graph Neural Simulators via Hamiltonian Dynamics

Tai Hoang¹, Alessandro Trenta^*,2, Alessio Gravina^*,2, Niklas Freymuth¹, Philipp Becker¹, Davide Bacciu², Gerhard Neumann¹

¹Karlsruhe Institute of Technology (KIT) | ²University of Pisa | ^*Equal contribution

Published at the International Conference on Learning Representations (ICLR) 2026

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Quick Start

Prerequisites

• Python 3.10.13
• uv

Installation

uv venv --python 3.10.13
source .venv/bin/activate
uv sync

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Dataset Setup

Download and extract datasets to ./dataset_public/:

Dataset	Source
PlateDeformation	Zenodo
SphereCloth	Zenodo
WaveBalls	Zenodo
Kuramoto-Sivashinsky	Zenodo
Impact Plate	HCMT
Cylinder Flow	MeshGraphNets

Note: These are raw datasets and should be stored under ./dataset_public/DATASET_NAME/raw

Verify:

python main.py -cn experiment/abaqus_plate_deformation_matching trainer.max_epochs=1 dataset.train_n_sequences=5

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Usage

# Specific environments
python main.py -cn experiment/abaqus_plate_deformation_matching
python main.py -cn experiment/sphere_cloth_matching
python main.py -cn experiment/wave_balls_matching
python main.py -cn experiment/kuramoto_matching
python main.py -cn experiment/impact_plate_matching
python main.py -cn experiment/cylinder_flow_matching

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Citation

If you find this work useful, please cite our paper:

@inproceedings{
  hoang2026igns,
  title={Improving Long-Range Interactions in Graph Neural Simulators via Hamiltonian Dynamics},
  author={Hoang, Tai and Trenta, Alessandro and Gravina, Alessio and 
          Freymuth, Niklas and Becker, Philipp and Bacciu, Davide and Neumann, Gerhard},
  booktitle={The Fourteenth International Conference on Learning Representations},
  year={2026},
  url={https://openreview.net/forum?id=x66u6TEDUw}
}

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