  Recently, physics-driven deep learning methods have shown particular promise
for the prediction of physical fields, especially to reduce the dependency on
large amounts of pre-computed training data. In this work, we target the
physics-driven learning of complex flow fields with high resolutions. We
propose the use of \emph{Convolutional neural networks} (CNN) based U-net
architectures to efficiently represent and reconstruct the input and output
fields, respectively. By introducing Navier-Stokes equations and boundary
conditions into loss functions, the physics-driven CNN is designed to predict
corresponding steady flow fields directly. In particular, this prevents many of
the difficulties associated with approaches employing fully connected neural
networks. Several numerical experiments are conducted to investigate the
behavior of the CNN approach, and the results indicate that a first-order
accuracy has been achieved. Specifically for the case of a flow around a
cylinder, different flow regimes can be learned and the adhered "twin-vortices"
are predicted correctly. The numerical results also show that the training for
multiple cases is accelerated significantly, especially for the difficult cases
at low Reynolds numbers, and when limited reference solutions are used as
supplementary learning targets.

Fluid Dynamics;Computational Physics