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Efficient n-body simulations using physics informed graph neural networks

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

TL;DR

The paper tackles the high computational cost of gravitational $N$-body simulations by combining a leapfrog-based physical data generator with a graph neural network that regresses particle accelerations on a proximity graph. It uses an EdgeConv-inspired GNN with node/edge encoders, multiple message-passing layers, and a residual update to predict accelerations in 3D, trained on 60 simulated scenarios and evaluated on 6 test cases, across $3$ to $500$ bodies for $1000$ steps. The results show extremely low stepwise losses ($\sim10^{-14}$ to $10^{-13}$) and near-constant acceleration error over rollout, with negligible accumulated errors in position and velocity, and a practical speedup of about $1.17\times$ over baseline simulations. This work demonstrates the feasibility of physics-informed graph learning to accelerate complex dynamical simulations while maintaining fidelity, and it points to scalable extensions via sparse graphs, hierarchical modeling, and specialized handling of dominant bodies for larger systems.

Abstract

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.

Efficient n-body simulations using physics informed graph neural networks

TL;DR

The paper tackles the high computational cost of gravitational -body simulations by combining a leapfrog-based physical data generator with a graph neural network that regresses particle accelerations on a proximity graph. It uses an EdgeConv-inspired GNN with node/edge encoders, multiple message-passing layers, and a residual update to predict accelerations in 3D, trained on 60 simulated scenarios and evaluated on 6 test cases, across to bodies for steps. The results show extremely low stepwise losses ( to ) and near-constant acceleration error over rollout, with negligible accumulated errors in position and velocity, and a practical speedup of about over baseline simulations. This work demonstrates the feasibility of physics-informed graph learning to accelerate complex dynamical simulations while maintaining fidelity, and it points to scalable extensions via sparse graphs, hierarchical modeling, and specialized handling of dominant bodies for larger systems.

Abstract

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.

Paper Structure

This paper contains 20 sections, 7 equations, 3 figures, 1 table, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related works
  3. Methodology
  4. Data generation from physical simulation
  5. Gravitational acceleration formula
  6. Dataset generation
  7. Transformation to graph structure
  8. Model architecture and inference
  9. Initial features transformation
  10. Message passing and aggregation
  11. Message function
  12. Aggregation and update
  13. Regarding depth and receptive field
  14. Output layer and mapping to the regression task
  15. Training and evaluation
  16. ...and 5 more sections

Figures (3)

  • Figure 1: Results of the error analysis (left) and average scene execution time (right) for $1000$ simulation steps performed using the model.
  • Figure 2: Evolution of the in position, velocity, and acceleration over $1000$ simulation steps. The value at each step is the average of the values for all particles across all scenarios for that step.
  • Figure 3: Accumulated errors in position (left), velocity (centre) and acceleration (right). The error accumulation is shown for each of the $6$ scenes, from the one with the fewest particles (scene $0$, $3$ bodies) to that with the most particles (scene $5$, $500$).