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

While modern machine-learning techniques are generally considered data-hungry, it may not be the case for turbulence as each of its snapshots is likely to hold a greater amount of information than those studies in image science. In this talk, we discuss how nonlinear machine learning can efficiently extract physical insights even from a single snapshot of a turbulent vortical flow. We perform machine-learning-based super-resolution analysis, that reconstructs a high-resolution field from low-resolution data for an example of two-dimensional decaying turbulence. We find that vortical structures across a range of Reynolds numbers can be reconstructed from grossly coarse data using a carefully designed convolutional neural network trained with flow tiles sampled from only a single snapshot. Our results show that nonlinear machine learning can leverage scale-invariant properties to efficiently learn turbulent flows. We further present that training data of turbulent flows can be efficiently collected from a single snapshot by incorporating prior knowledge of their statistical characteristics.