  Convolutional neural networks (CNNs) have recently been applied to predict or
model fluid dynamics. However, mechanisms of CNNs for learning fluid dynamics
are still not well understood, while such understanding is highly necessary to
optimize the network or to reduce trial-and-errors during the network
optmization. In the present study, a CNN to predict future three-dimensional
unsteady wake flow using flow fields in the past occasions is developed.
Mechanisms of the developed CNN for prediction of wake flow behind a circular
cylinder are investigated in two flow regimes: the three-dimensional wake
transition regime and the shear-layer transition regime. Feature maps in the
CNN are visualized to compare flow structures which are extracted by the CNN
from flow at the two flow regimes. In both flow regimes, feature maps are found
to extract similar sets of flow structures such as braid shear-layers and
shedding vortices. A Fourier analysis is conducted to investigate mechanisms of
the CNN for predicting wake flow in flow regimes with different wave number
characteristics. It is found that a convolution layer in the CNN integrates and
transports wave number information from flow to predict the dynamics.
Characteristics of the CNN for transporting input information including time
histories of flow variables is analyzed by assessing contributions of each flow
variable and time history to feature maps in the CNN. Structural similarities
between feature maps in the CNN are calculated to reveal the number of feature
maps that contain similar flow structures. By reducing the number of feature
maps that contain similar flow structures, it is also able to successfully
reduce the number of parameters to learn in the CNN by 85\% without affecting
prediction performances.
