# Single-snapshot machine learning for super-resolution of turbulence

arXiv: https://arxiv.org/abs/2409.04923 · HTML: https://mlsanity.com/paper/2409.04923/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 29 references that are in the map.
- First posted on arXiv 7 Sep 2024.

## Builds on (most cited first, 5 of 5)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Convolutional-network models to predict wall-bounded turbulence from wall quantities](https://mlsanity.com/paper/2006.12483/) (2020)
- [Super-Resolution Analysis via Machine Learning: A Survey for Fluid Flows](https://mlsanity.com/paper/2301.10937/) (2023)
- [Image and video compression of fluid flow data](https://mlsanity.com/paper/2301.00078/) (2022)

## Built on by (most cited first, 9 of 9)

- [Guiding diffusion models to reconstruct flow fields from sparse data](https://mlsanity.com/paper/2510.19971/) (2025)
- [SIMR-NO: A Spectrally-Informed Multi-Resolution Neural Operator for Turbulent Flow Super-Resolution](https://mlsanity.com/paper/2603.28073/) (2026)
- [Guided Unconditional and Conditional Generative Models for Super-Resolution and Inference of Quasi-Geostrophic Turbulence](https://mlsanity.com/paper/2507.00719/) (2025)
- [Super-resolution of turbulent reacting flows on complex meshes using graph neural networks](https://mlsanity.com/paper/2603.01080/) (2026)
- [Pixel-Resolved Long-Context Learning for Turbulence at Exascale: Resolving Small-scale Eddies Toward the Viscous Limit](https://mlsanity.com/paper/2507.16697/) (2025)
- [Patch-Based 3D Variational Autoencoder for Super-Resolution of Turbulent Channel Flow](https://mlsanity.com/paper/2507.22082/) (2025)
- [Fourier-Invertible Neural Encoder (FINE) for Homogeneous Flows](https://mlsanity.com/paper/2505.15329/) (2025)
- [Implicit Augmentation from Distributional Symmetry in Turbulence Super-Resolution](https://mlsanity.com/paper/2509.20683/) (2025)
- [Extreme-Scale Super-Resolution of Homogeneous Turbulence from a Single Realization](https://mlsanity.com/paper/2610.20305/) (2026)

## Abstract (arXiv)

Modern machine-learning techniques are generally considered data-hungry. However, this may not be the case for turbulence as each of its snapshots can hold more information than a single data file in general machine-learning settings. This study asks the question of whether nonlinear machine-learning techniques can effectively extract physical insights even from as little as a it single snapshot of turbulent flow. As an example, we consider machine-learning-based super-resolution analysis that reconstructs a high-resolution field from low-resolution data for two examples of two-dimensional isotropic turbulence and three-dimensional turbulent channel flow. First, we reveal that a carefully designed machine-learning model trained with flow tiles sampled from only a single snapshot can reconstruct vortical structures across a range of Reynolds numbers for two-dimensional decaying turbulence. Successful flow reconstruction indicates that nonlinear machine-learning techniques can leverage scale-invariance properties to learn turbulent flows. We also show that training data of turbulent flows can be cleverly collected from a single snapshot by considering characteristics of rotation and shear tensors. Second, we perform the single-snapshot super-resolution analysis for turbulent channel flow, showing that it is possible to extract physical insights from a single flow snapshot even with inhomogeneity. The present findings suggest that embedding prior knowledge in designing a model and collecting data is important for a range of data-driven analyses for turbulent flows. More broadly, this work hopes to stop machine-learning practitioners from being wasteful with turbulent flow data.