用图神经网络加速天体模拟，精度高且长期稳定。
Efficient n-body simulations using physics informed graph neural networks
- 结合物理约束的图神经网络预测粒子加速度
- 500体模拟1000步误差极小，位置速度加速度累积误差可忽略
- 比传统方法快17%，适合需要高效高精度仿真的研究者
本文提出一种新方法，通过将物理信息图神经网络（GNN）与传统数值方法结合，加速n体模拟。采用基于跳跃蛙法的模拟引擎生成多样天体场景数据，并转换为图结构表示。训练定制化GNN以高精度预测粒子加速度。在60个训练和6个测试模拟上进行实验，涵盖3至500个粒子，持续1000个时间步。结果表明，该模型预测误差极低，位置、速度和加速度的累积误差保持微不足道，同时相比传统方法实现约17%的计算加速。这证明深度学习与物理模拟融合是提升计算效率且不牺牲精度的可行路径。
原文摘要 · Abstract (English)
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.
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