  Physics-informed deep learning has drawn tremendous interest in recent years
to solve computational physics problems, whose basic concept is to embed
physical laws to constrain/inform neural networks, with the need of less data
for training a reliable model. This can be achieved by incorporating the
residual of physics equations into the loss function. Through minimizing the
loss function, the network could approximate the solution. In this paper, we
propose a mixed-variable scheme of physics-informed neural network (PINN) for
fluid dynamics and apply it to simulate steady and transient laminar flows at
low Reynolds numbers. A parametric study indicates that the mixed-variable
scheme can improve the PINN trainability and the solution accuracy. The
predicted velocity and pressure fields by the proposed PINN approach are also
compared with the reference numerical solutions. Simulation results demonstrate
great potential of the proposed PINN for fluid flow simulation with a high
accuracy.
