  In the recent application of scientific modeling, machine learning models are
largely applied to facilitate computational simulations of fluid systems.
Rotation symmetry is a general property for most symmetric fluid systems.
However, in general, current machine learning methods have no theoretical way
to guarantee rotational symmetry. By observing an important property of
contraction and rotation operation on high-order symmetric tensors, we prove
that the rotation operation is preserved via tensor contraction. Based on this
theoretical justification, in this paper, we introduce Rotation-Equivariant
Network (RotEqNet) to guarantee the property of rotation-equivariance for
high-order tensors in fluid systems. We implement RotEqNet and evaluate our
claims through four case studies on various fluid systems. The property of
error reduction and rotation-equivariance is verified in these case studies.
Results from the comparative study show that our method outperforms
conventional methods, which rely on data augmentation.
