Learning Lagrangian Fluid Mechanics with E($3$)-Equivariant Graph Neural Networks
This work addresses the need for more accurate dynamic-interaction models in machine learning for engineering systems, specifically in fluid mechanics, though it is incremental as it builds on existing equivariant graph neural networks.
The authors tackled the problem of learning Lagrangian fluid mechanics by comparing equivariant graph neural networks to non-equivariant ones, finding that their proposed history embeddings in equivariant models led to more accurate physical interactions, as benchmarked on 3D decaying Taylor-Green vortex and 3D reverse Poiseuille flow with measures like kinetic energy and Sinkhorn distance.
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.