  We investigate the applicability of machine learning based reduced order
model (ML-ROM) to three-dimensional complex flows. As an example, we consider a
turbulent channel flow at the friction Reynolds number of $Re_\tau=110$ in a
minimum domain which can maintain coherent structures of turbulence. Training
data set are prepared by direct numerical simulation (DNS). The present ML-ROM
is constructed by combining a three-dimensional convolutional neural network
autoencoder (CNN-AE) and a long short-term memory (LSTM). The CNN-AE works to
map high-dimensional flow fields into a low-dimensional latent space. The LSTM
is then utilized to predict a temporal evolution of the latent vectors obtained
by the CNN-AE. The combination of CNN-AE and LSTM can represent the
spatio-temporal high-dimensional dynamics of flow fields by only integrating
the temporal evolution of the low-dimensional latent dynamics. The turbulent
flow fields reproduced by the present ML-ROM show statistical agreement with
the reference DNS data in time-ensemble sense, which can also be found through
an orbit-based analysis. Influences of the population of vortical structures
contained in the domain and the time interval used for temporal prediction on
the ML- ROM performance are also investigated. The potential and limitation of
the present ML-ROM for turbulence analysis are discussed at the end of our
presentation.
