Learning Lagrangian Fluid Mechanics with E($3$)-Equivariant Graph Neural
  Networks
Artur P. Toshev Gianluca Galletti Johannes Brandstetter Stefan Adami Nikolaus A. Adams
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.