E($3$) Equivariant Graph Neural Networks for Particle-Based Fluid Mechanics
This work addresses the need for more accurate machine learning models in engineering systems, specifically for particle-based fluid mechanics, but it is incremental as it builds on existing equivariant graph neural network methods.
The authors tackled the problem of learning dynamic-interaction models for fluid mechanics by comparing equivariant graph neural networks to non-equivariant ones, finding that equivariant models learn more physically accurate interactions, as benchmarked on 3D fluid flow systems 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 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.