Single-snapshot machine learning for super-resolution of turbulence

Abstract

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.

To appear in Journal of Fluid Mechanics

References in corpus (13)

• Machine Learning for Fluid Mechanics
• Turbulence Modeling in the Age of Data
• Direct numerical simulation of turbulent channel flow up to $R{e}_{\tau }\approx 5200$
• Super-resolution reconstruction of turbulent flows with machine learning
• Data-driven prediction of unsteady flow fields over a circular cylinder using deep learning
• Machine learning based spatio-temporal super resolution reconstruction of turbulent flows
• Unsupervised deep learning for super-resolution reconstruction of turbulence
• Super-Resolution Analysis via Machine Learning: A Survey for Fluid Flows
• Network Structure of Two-Dimensional Decaying Isotropic Turbulence
• A transformer-based synthetic-inflow generator for spatially-developing turbulent boundary layers
• Data-driven nonlinear turbulent flow scaling with Buckingham Pi variables
• Three-dimensional generative adversarial networks for turbulent flow estimation from wall measurements
• Image and video compression of fluid flow data

Cited by in corpus (5)

• Compressing fluid flows with nonlinear machine learning: mode decomposition, latent modeling, and flow control
• Super-resolution reconstruction of turbulent flows from a single Lagrangian trajectory
• Machine-learning-based simulation of turbulent flows over periodic hills using a hybrid U-Net and Fourier neural operator framework
• Extracting self-similarity from data
• Guided Unconditional and Conditional Generative Models for Super-Resolution and Inference of Quasi-Geostrophic Turbulence