2025/09/25 by Julia Balla, Balla, Julia, Jeremiah Bailey +11 · 1 citation
Computer Science · Engineering · Environmental Science · #Advanced Image Processing Techniques #Anisotropy #Boundary (topology) #Convolutional neural network #FOS: Computer and information sciences #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Isotropy #Machine Learning (cs.LG) #Rotational invariance #Rotational symmetry #Symmetry (geometry) #Turbulence #Wind and Air Flow Studies
paper · pdf · doi:10.48550/arxiv.2509.20683
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2025/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The immense computational cost of simulating turbulence has motivated the use of machine learning approaches for super-resolving turbulent flows. A central challenge is ensuring that learned models respect physical symmetries, such as rotational equivariance. We show that standard convolutional neural networks (CNNs) can partially acquire this symmetry without explicit augmentation or specialized architectures, as turbulence itself provides implicit rotational augmentation in both time and space. Using 3D channel-flow subdomains with differing anisotropy, we find that models trained on more isotropic mid-plane data achieve lower equivariance error than those trained on boundary layer data, and that greater temporal or spatial sampling further reduces this error. We show a distinct scale-dependence of equivariance error that occurs regardless of dataset anisotropy that is consistent with Kolmogorov's local isotropy hypothesis. These results clarify when rotational symmetry must be explicitly incorporated into learning algorithms and when it can be obtained directly from turbulence, enabling more efficient and symmetry-aware super-resolution.