  In this paper, an end-to-end nonlinear model reduction methodology is
presented based on the convolutional recurrent autoencoder networks. The
methodology is developed in the context of the overall data-driven
reduced-order model framework proposed in the paper. The basic idea behind the
methodology is to obtain the low dimensional representations via convolutional
neural networks and evolve these low dimensional features via recurrent neural
networks in the time domain. The high dimensional representations are
constructed from the evolved low dimensional features via transpose
convolutional neural networks. With an unsupervised training strategy, the
model serves as an end to end tool which can evolve the flow state of the
nonlinear dynamical system. The convolutional recurrent autoencoder network
model is applied to the problem of flow past bluff bodies for the first time.
To demonstrate the effectiveness of the methodology, two canonical problems
namely the flow past a plain cylinder and the flow past side-by-side cylinders
are explored in this paper. Pressure and velocity fields of the unsteady flow
are predicted in future via the convolutional recurrent autoencoder model. The
performance of the model is satisfactory for both the problems. Specifically,
the multiscale nature and the gap flow dynamics of the side-by-side cylinders
are captured by the proposed data-driven model reduction methodology. The error
metrics, the normalized squared error, and the normalized reconstruction error
are considered for the assessment of the data-driven framework.
