RotEqNet: Rotation-Equivariant Network for Fluid Systems with Symmetric High-Order Tensors
This addresses the challenge of maintaining rotation symmetry in fluid simulations for scientific modeling, offering a theoretical and practical improvement over data augmentation-based approaches.
The paper tackles the problem of ensuring rotational symmetry in machine learning models for fluid systems by introducing RotEqNet, a rotation-equivariant network for high-order tensors, and shows it outperforms conventional methods with data augmentation in error reduction and equivariance across four case studies.
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.