  Unsteady flow fields over a circular cylinder are trained and predicted using
four different deep learning networks: convolutional neural networks with and
without consideration of conservation laws, generative adversarial networks
with and without consideration of conservation laws. Flow fields at future
occasions are predicted based on information of flow fields at previous
occasions. Deep learning networks are trained first using flow fields at
Reynolds numbers of 100, 200, 300, and 400, while flow fields at Reynolds
numbers of 500 and 3000 are predicted using the trained deep learning networks.
Physical loss functions are proposed to explicitly impose information of
conservation of mass and momentum to deep learning networks. An adversarial
training is applied to extract features of flow dynamics in an unsupervised
manner. Effects of the proposed physical loss functions, adversarial training,
and network sizes on the prediction accuracy are analyzed. Predicted flow
fields using deep learning networks are in favorable agreement with flow fields
computed by numerical simulations.
