Studying turbulent flows with physics-informed neural networks and sparse data

Abstract

Physics-informed neural networks (PINNs) have recently become a viable modelling method for the scientific machine-learning community. The appeal of this network architecture lies in the coupling of a deep neural network (DNN) with partial differential equations (PDEs): the DNN can be considered a universal function approximator, and the physical knowledge from the embedded PDEs regularises the network during training. This regularisation improves robustness of the network and means the network only requires sparse training data in the domain. We apply PINNs with embedded Reynolds-averaged Navier–Stokes (RANS) equations to a spatially developing adverse-pressure-gradient (APG) boundary layer..