This article introduces a new Neural Network stochastic model to generate a 1-dimensional stochastic field with turbulent velocity statistics. Both the model architecture and training procedure ground on the Kolmogorov and Obukhov statistical theories of fully developed turbulence, so guaranteeing descriptions of 1) energy distribution, 2) energy cascade and 3) intermittency across scales in agreement with experimental observations. The model is a Generative Adversarial Network with multiple multiscale optimization criteria. First, we use three physics-based criteria: the variance, skewness and flatness of the increments of the generated field that retrieve respectively the turbulent energy distribution, energy cascade and intermittency across scales. Second, the Generative Adversarial Network criterion, based on reproducing statistical distributions, is used on segments of different length of the generated field. Furthermore, to mimic multiscale decompositions frequently used in turbulence's studies, the model architecture is fully convolutional with kernel sizes varying along the multiple layers of the model. To train our model we use turbulent velocity signals from grid turbulence at Modane wind tunnel.

翻译：本文提出了一种新的神经网络随机模型，用于生成具有湍流速度统计特性的一维随机场。该模型的架构和训练过程均基于科莫戈罗夫和奥布霍夫关于充分发展湍流的统计理论，从而确保对以下三个方面的描述与实验观测一致：1）能量分布，2）能量级联，3）跨尺度的间歇性。该模型是一种具有多个多尺度优化准则的生成对抗网络。首先，我们采用三个基于物理的准则：生成场增量的方差、偏度和峰度，它们分别用于还原跨尺度的湍流能量分布、能量级联和间歇性。其次，基于统计分布复现的生成对抗网络准则被应用于生成场不同长度的片段上。此外，为模拟湍流研究中常用的多尺度分解，该模型架构采用全卷积设计，且卷积核大小沿模型多个层级变化。为训练模型，我们使用了来自莫达纳风洞网格湍流的湍流速度信号。