Efficient n-body simulations using physics informed graph neural networks

This paper presents a novel approach for accelerating n-body simulations by integrating a physics-informed graph neural networks (GNN) with traditional numerical methods. Our method implements a leapfrog-based simulation engine to generate datasets from diverse astrophysical scenarios which are then transformed into graph representations. A custom-designed GNN is trained to predict particle accelerations with high precision. Experiments, conducted on 60 training and 6 testing simulations spanning from 3 to 500 bodies over 1000 time steps, demonstrate that the proposed model achieves extremely low prediction errors-loss values while maintaining robust long-term stability, with accumulated errors in position, velocity, and acceleration remaining insignificant. Furthermore, our method yields a modest speedup of approximately 17% over conventional simulation techniques. These results indicate that the integration of deep learning with traditional physical simulation methods offers a promising pathway to significantly enhance computational efficiency without compromising accuracy.

@article{ramos-osuna2025_2504.01169,
  title={ Efficient n-body simulations using physics informed graph neural networks },
  author={ Víctor Ramos-Osuna and Alberto Díaz-Álvarez and Raúl Lara-Cabrera },
  journal={arXiv preprint arXiv:2504.01169},
  year={ 2025 }
}