mlsanityData to 7 Oct 2026

Rotationally Equivariant Super-Resolution of Velocity Fields in Two-Dimensional Fluids Using Convolutional Neural Networks

arXiv 2202.11099 ↗First posted 22 Feb 2022physics.flu-dyn cs.CV physics.ao-phcited by 3

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Abstract (arXiv)

This paper investigates the super-resolution (SR) of velocity fields in two-dimensional fluids from the viewpoint of rotational equivariance. SR refers to techniques that estimate high-resolution images from those in low resolution and has lately been applied in fluid mechanics. The rotational equivariance of SR models is defined as the property in which the super-resolved velocity field is rotated according to a rotation of the input, which leads to the inference covariant to the orientation of fluid systems. Generally, the covariance in physics is related to symmetries. To clarify a relationship to symmetries, the rotational consistency of datasets for SR is newly introduced as the invariance of pairs of low- and high-resolution velocity fields with respect to rotation. This consistency is sufficient and necessary for SR models to acquire rotational equivariance from large datasets with supervised learning. Such a large dataset is not required when rotational equivariance is imposed on SR models through weight sharing of convolution kernels as prior knowledge. Even if a fluid system has rotational symmetry, this symmetry may not carry over to a velocity dataset, which is not rotationally consistent. This inconsistency can occur when the rotation does not commute with the generation of low-resolution velocity fields. These theoretical suggestions are supported by the results from numerical experiments, where two existing convolutional neural networks (CNNs) are converted into rotationally equivariant CNNs and the inferences of the four CNNs are compared after the supervised training.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 46 of its 98 references that are in the map. First posted on arXiv 22 Feb 2022.

Builds on

46 of 98 references.

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Cited by year

Citing papers per year: 2024: 1; 2025: 2.

3 papers.

  1. 2024Spatially-Aware Diffusion Models with Cross-Attention for Global Field Reconstruction with Sparse Observationscited by 13
  2. 2025Surrogate Modeling of 3D Rayleigh-Benard Convection with Equivariant Autoencoderscited by 3
  3. 2025Implicit Augmentation from Distributional Symmetry in Turbulence Super-Resolutioncited by 0