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 applications. This study asks the question of whether nonlinear machine-learning techniques can effectively extract physical insights even from as little as a single snapshot of a turbulent vortical flow. As an example, we consider machine-learning-based super-resolution analysis that reconstructs a high-resolution field from low-resolution data for two-dimensional decaying turbulence. 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. Successful flow reconstruction indicates that nonlinear machine-learning techniques can leverage scale-invariance properties to learn turbulent flows. We further show that training data of turbulent flows can be cleverly collected from a single snapshot by considering characteristics of rotation and shear tensors. 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.

本研究解决了机器学习对数据需求过高的问题，通过探讨如何仅使用单一湍流快照提取物理特征。研究显示，精心设计的机器学习模型能够成功重建从低分辨率数据中提取的高分辨率湍流结构，表明非线性机器学习技术在学习湍流流动方面具有潜力。此成果预示着在设计模型和数据收集时融入先验知识的重要性，从而提高对湍流流动的数据利用效率。

单快照机器学习在湍流超分辨率中的应用