# Efficient n-body simulations using physics informed graph neural networks

arXiv: https://arxiv.org/abs/2504.01169 · HTML: https://mlsanity.com/paper/2504.01169/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 21 references that are in the map.
- First posted on arXiv 1 Apr 2025.

## Builds on (most cited first, 9 of 9)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [DeeperGCN: All You Need to Train Deeper GCNs](https://mlsanity.com/paper/2006.07739/) (2020)

## Abstract (arXiv)

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.