A multiscale and multicriteria Generative Adversarial Network to
  synthesize 1-dimensional turbulent fields
Carlos Granero-Belinchon Manuel Cabeza Gallucci
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.