# RotEqNet: Rotation-Equivariant Network for Fluid Systems with Symmetric High-Order Tensors

arXiv: https://arxiv.org/abs/2005.04286 · HTML: https://mlsanity.com/paper/2005.04286/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Apr 2020.

## Built on by (most cited first, 4 of 4)

- [Importance of equivariant and invariant symmetries for fluid flow modeling](https://mlsanity.com/paper/2307.05486/) (2023)
- [Rotationally Equivariant Super-Resolution of Velocity Fields in Two-Dimensional Fluids Using Convolutional Neural Networks](https://mlsanity.com/paper/2202.11099/) (2022)
- [Structure Preserving Diffusion Models](https://mlsanity.com/paper/2402.19369/) (2024)
- [Permutation Equivariant Neural Networks for Symmetric Tensors](https://mlsanity.com/paper/2503.11276/) (2025)

## Abstract (arXiv)

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.