Efficient n-body simulations using physics informed graph neural networks

Alberto Díaz-Álvarez, Víctor Ramos Osuna, Raúl Lara-Cabrera

Keywords: N-body simulation, Graph Neural Networks, Physics-informed modeling, Optimization, Deep learning

TL;DR: A physics-informed graph neural network speeds up N-body simulations without (almost) sacrificing accuracy.

Abstract: This paper presents a novel approach for accelerating N-bodies 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 maintains 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.

Submission Number: 29