  Deep learning method has attracted tremendous attention to handle fluid
dynamics in recent years. However, the deep learning method requires much data
to guarantee the generalization ability and the data of fluid dynamics are
deficient. Recently, physics informed neural network (PINN) is popular to solve
the fluid flow problems, which basic concept is to embed the governing equation
and continuity equation into loss function, with the requirement of less
dataset for obtaining a reliable neural network. In this paper, the
mixed-variable PINN method, which convert the governing equation into continuum
and constitutive formulations, is proposed to solve the fluid dynamics (flow
past cylinder) without any labeled data. The initial/boundary conditions with
penalty factors are also embedded into the loss function to become a
well-imposed problem. The results show that mixed-variable PINN has better
predictive ability to construct the flow field than traditional PINN scheme.
Furthermore, the transfer learning method is adopted to is solve the fluid
solutions with different Reynold numbers with less computational cost. The
results also demonstrate that the transfer learning method can well simulate
the different Reynolds number in a short time.
