  We propose a method to construct a reduced order model with machine learning
for unsteady flows. The present machine-learned reduced order model (ML-ROM) is
constructed by combining a convolutional neural network autoencoder (CNN-AE)
and a long short-term memory (LSTM), which are trained in a sequential manner.
First, the CNN-AE is trained using direct numerical simulation (DNS) data so as
to map the high-dimensional flow data into low-dimensional latent space. Then,
the LSTM is utilized to establish a temporal prediction system for the
low-dimensionalized vectors obtained by CNN-AE. As a test case, we consider
flows around a bluff body whose shape is defined using a combination of
trigonometric functions with random amplitudes. The present ML-ROMs are trained
on a set of 80 bluff body shapes and tested on a different set of 20 bluff body
shapes not used for training, with both training and test shapes chosen from
the same random distribution. The flow fields are confirmed to be well
reproduced by the present ML-ROM in terms of various statistics. We also focus
on the influence of two main parameters: (1) the latent vector size in the
CNN-AE, and (2) the time step size between the mapped vectors used for the
LSTM. The present results show that the ML-ROM works well even for unseen
shapes of bluff bodies when these parameters are properly chosen, which implies
great potential for the present type of ML-ROM to be applied to more complex
flows
