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.

采用等变图神经网络比其非等变神经网络在动态交互模型中能够更准确地学习流体力学系统的运动，并发现等变模型可以对湍流流量进行粗粒化建模和参数推广。