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

TL;DR

This paper demonstrates that E(3) equivariant graph neural networks can learn more physically accurate fluid dynamics models than non-equivariant ones, though at the cost of increased training time, with implications for turbulence modeling.

Contribution

The paper introduces the use of E(3) equivariant graph neural networks for modeling particle-based fluid mechanics, showing improved physical accuracy over non-equivariant models.

Findings

Equivariant models outperform non-equivariant models in physical accuracy.

Equivariant models are slower to train and evaluate.

Potential for coarse-grained turbulence models and better generalization.

Abstract

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.