Physics-informed deep learning for incompressible laminar flows

Physics-informed deep learning (PIDL) has drawn tremendous interest in recent years to solve computational physics problems. The basic concept of PIDL is to embed available physical laws to constrain/inform neural networks, with the need of less rich data for training a reliable model. This can be achieved by incorporating the residual of the partial differential equations and the initial/boundary conditions into the loss function. Through minimizing the loss function, the neural network would be able to approximate the solution to the physical field of interest. 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. The predicted velocity and pressure fields by the proposed PINN approach are compared with the reference numerical solutions. Simulation results demonstrate great potential of the proposed PINN for fluid flow simulation with a high accuracy.