The physical complexity and the large number of degrees of freedom that can be resolved today by direct numerical simulations of turbulent flows, and by the most sophisticated experimental techniques, require new strategies to reduce and analyse the data so generated, and to model the turbulent behaviour. We discuss a few concrete examples for which the turbulence data have been analysed by machine learning tools. We also comment on work in neighbouring fields of physics, particularly astrophysical (and astronomical) work, where Big Data has been the paradigm for some time. We discuss unsupervised, semi-supervised and supervised machine learning methods to direct numerical simulations data of homogeneous isotropic turbulence, Rayleigh-Bénard convection, and the minimal flow unit of a turbulent channel flow; for the last case, we discuss in some detail the application of echo state networks, this being one implementation of reservoir computing. The paper also provides a brief perspective on machine learning applications more broadly.

中文翻译：

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湍流中机器学习的观点

今天可以通过湍流的直接数值模拟和最复杂的实验技术解决的物理复杂性和大量自由度，需要新的策略来减少和分析如此产生的数据，并模拟湍流行为. 我们讨论了一些具体的例子，通过机器学习工具分析了湍流数据。我们还评论了邻近物理学领域的工作，特别是天体物理学（和天文）工作，其中大数据已经成为范式有一段时间了。我们讨论了无监督、半监督和有监督的机器学习方法，以指导均匀各向同性湍流、瑞利-贝纳对流和湍流通道流的最小流动单位的数值模拟数据；对于最后一种情况，我们详细讨论了回声状态网络的应用，这是水库计算的一种实现。该论文还提供了更广泛的机器学习应用的简要观点。