Physics-informed neural networks for periodic flows

Physics-informed neural network (PINN) is a neural network that combines machine learning methods with the physics of the problem often expressed in terms of differential equations along with boundary/initial conditions. In this paper, we employed unsupervised PINNs to solve steady-state incompressible laminar periodic flow problems without using any data. First, the PINN code for periodic flows was verified using flow between parallel plates. Further, two geometries were considered in this paper: periodic flow over cylinders between parallel plates and periodic flows through wavy channels, up to a maximum Reynolds number of 400. The proposed approach showed excellent results when compared to grid-independent computational fluid dynamics results with maximum L2-norm error of O(10−2) and O(10−1) for streamwise and cross-stream velocity, respectively.