We define and study a fully-convolutional neural network stochastic model, NN-Turb, which generates a 1-dimensional field with some turbulent velocity statistics. In particular, the generated process satisfies the Kolmogorov 2/3 law for second order structure function. It also presents negative skewness across scales (i.e. Kolmogorov 4/5 law) and exhibits intermittency as characterized by skewness and flatness. Furthermore, our model is never in contact with turbulent data and only needs the desired statistical behavior of the structure functions across scales for training.

翻译：我们定义并研究了一种全卷积神经网络随机模型NN-Turb，该模型能够生成具有特定湍流速度统计特征的一维场。具体而言，该生成过程满足二阶结构函数的柯尔莫哥洛夫2/3定律，同时呈现跨尺度的负偏度（即柯尔莫哥洛夫4/5定律），并表现出以偏度和平坦度为特征的间歇性。此外，我们的模型从未接触过湍流数据，仅需结构函数在各尺度上的目标统计行为即可完成训练。