# Scalable Graph Networks for Particle Simulations

arXiv: https://arxiv.org/abs/2010.06948 · HTML: https://mlsanity.com/paper/2010.06948/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Oct 2020.

## Built on by (most cited first, 8 of 8)

- [Equivariant Graph Mechanics Networks with Constraints](https://mlsanity.com/paper/2203.06442/) (2022)
- [Equivariant Graph Neural Operator for Modeling 3D Dynamics](https://mlsanity.com/paper/2401.11037/) (2024)
- [Boundary Graph Neural Networks for 3D Simulations](https://mlsanity.com/paper/2106.11299/) (2021)
- [Grounding Graph Network Simulators using Physical Sensor Observations](https://mlsanity.com/paper/2302.11864/) (2023)
- [Physics-Informed Regularization for Domain-Agnostic Dynamical System Modeling](https://mlsanity.com/paper/2410.06366/) (2024)
- [Towards Complex Dynamic Physics System Simulation with Graph Neural ODEs](https://mlsanity.com/paper/2305.12334/) (2023)
- [Flexible Networks for Learning Physical Dynamics of Deformable Objects](https://mlsanity.com/paper/2112.03728/) (2021)
- [Towards Learning Self-Organized Criticality of Rydberg Atoms using Graph Neural Networks](https://mlsanity.com/paper/2207.08927/) (2022)

## Abstract (arXiv)

Learning system dynamics directly from observations is a promising direction in machine learning due to its potential to significantly enhance our ability to understand physical systems. However, the dynamics of many real-world systems are challenging to learn due to the presence of nonlinear potentials and a number of interactions that scales quadratically with the number of particles N, as in the case of the N-body problem. In this work, we introduce an approach that transforms a fully-connected interaction graph into a hierarchical one which reduces the number of edges to O(N). This results in linear time and space complexity while the pre-computation of the hierarchical graph requires O(Nlog (N)) time and O(N) space. Using our approach, we are able to train models on much larger particle counts, even on a single GPU. We evaluate how the phase space position accuracy and energy conservation depend on the number of simulated particles. Our approach retains high accuracy and efficiency even on large-scale gravitational N-body simulations which are impossible to run on a single machine if a fully-connected graph is used. Similar results are also observed when simulating Coulomb interactions. Furthermore, we make several important observations regarding the performance of this new hierarchical model, including: i) its accuracy tends to improve with the number of particles in the simulation and ii) its generalisation to unseen particle counts is also much better than for models that use all O(N2) interactions.