# E(3) Equivariant Graph Neural Networks for Particle-Based Fluid Mechanics

arXiv: https://arxiv.org/abs/2304.00150 · HTML: https://mlsanity.com/paper/2304.00150/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 22 references that are in the map.
- First posted on arXiv 31 Mar 2023.

## Builds on (most cited first, 10 of 10)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [Geometric and Physical Quantities Improve E(3) Equivariant Message Passing](https://mlsanity.com/paper/2110.02905/) (2021)
- [A multi-resolution SPH method for fluid-structure interactions](https://mlsanity.com/paper/1911.13255/) (2019)

## Built on by (most cited first, 7 of 7)

- [Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations](https://mlsanity.com/paper/2407.07218/) (2024)
- [A review of graph neural network applications in mechanics-related domains](https://mlsanity.com/paper/2407.11060/) (2024)
- [Enhancing the Scalability and Applicability of Kohn-Sham Hamiltonians for Molecular Systems](https://mlsanity.com/paper/2502.19227/) (2025)
- [E2Former: An Efficient and Equivariant Transformer with Linear-Scaling Tensor Products](https://mlsanity.com/paper/2501.19216/) (2025)
- [Advancing Molecular Graph-Text Pre-training via Fine-grained Alignment](https://mlsanity.com/paper/2409.14106/) (2024)
- [Approximate Equivariance via Projection-based Regularisation](https://mlsanity.com/paper/2601.05028/) (2026)
- [A Geometric Insight into Equivariant Message Passing Neural Networks on Riemannian Manifolds](https://mlsanity.com/paper/2310.10448/) (2023)

## Abstract (arXiv)

We contribute to the vastly growing field of machine learning for engineering systems by demonstrating that equivariant graph neural networks have the potential to learn more accurate dynamic-interaction models than their non-equivariant counterparts. We benchmark two well-studied fluid flow systems, namely the 3D decaying Taylor-Green vortex and the 3D reverse Poiseuille flow, and compare equivariant graph neural networks to their non-equivariant counterparts on different performance measures, such as kinetic energy or Sinkhorn distance. Such measures are typically used in engineering to validate numerical solvers. Our main findings are that while being rather slow to train and evaluate, equivariant models learn more physically accurate interactions. This indicates opportunities for future work towards coarse-grained models for turbulent flows, and generalization across system dynamics and parameters.