Neural network based generation of a 1-dimensional stochastic field with turbulent velocity statistics

TL;DR

This paper introduces NN-Turb, a neural network model that generates 1D turbulent velocity fields matching key statistical laws of turbulence without direct data contact.

Contribution

The paper presents a novel neural network model that reproduces turbulent velocity statistics solely based on desired statistical properties, without using turbulent data for training.

Findings

Successfully reproduces Kolmogorov 2/3 law

Exhibits negative skewness and intermittency

Operates without direct turbulent data contact

Abstract

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.