This dataset provides a set of 4 simulation tasks for testing long-range interactions in Graph Neural Simulators, used in our study on improving long-range interactions via Hamiltonian dynamics. The dataset is released to support reproducible evaluation and benchmarking of long-horizon information propagation in graph-based simulators. Code / training pipeline: https://github.com/thobotics/neural_pde_matching Citation If you use this dataset, please cite: @inproceedings{ hoang2026igns, title={Improving Long-Range Interactions in Graph Neural Simulators via Hamiltonian Dynamics}, author={Tai Hoang and Alessandro Trenta and Alessio Gravina and Niklas Freymuth and Philipp Becker and Davide Bacciu and Gerhard Neumann}, booktitle={The Fourteenth International Conference on Learning Representations}, year={2026}, url={https://openreview.net/forum?id=x66u6TEDUw},}