Learning Lagrangian Fluid Mechanics with E($3$)-Equivariant Graph Neural Networks

TL;DR

This paper demonstrates that E(3)-equivariant graph neural networks can learn more accurate fluid dynamics models than non-equivariant models, especially when using specific history embeddings, despite current training speed limitations.

Contribution

The study shows the effectiveness of E(3)-equivariant graph neural networks in modeling fluid systems and introduces new embedding methods for physical information histories.

Findings

Equivariant models outperform non-equivariant models in accuracy.

History embeddings improve physical interaction learning.

Equivariant models are currently slower to train and evaluate.

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 3D decaying Taylor-Green vortex and 3D reverse Poiseuille flow, and evaluate the models based on different performance measures, such as kinetic energy or Sinkhorn distance. In addition, we investigate different embedding methods of physical-information histories for equivariant models. We find that while currently being rather slow to train and evaluate, equivariant models with our proposed history embeddings learn more accurate physical interactions.