Data and physics-driven modeling for fluid flow with a physics-informed graph convolutional neural network

A physics-informed graph convolutional network (PINN-GCN) data-driven model was proposed to solve steady-state fluid flows with various geometries. A GCN guarantees a data-driven model that adapts to irregularly structured or unstructured mesh data. In addition, the mean squared residuals of the governing equations in partial differential forms and boundary conditions are introduced into the loss function of the network model, the Physics-Informed Neural Network (PINN) increases the knowledge of the physical rules of the model, enhances the model accuracy even with sparse training data. With nine training cases containing approximately 2000 spatial point data individually, PINN-GCN could accurately predict the physical flow field over a two-dimensional object of variable size, achieving above 98.6% for mean accuracy. With five training data cases, the model could predict flow over a cylinder with variable position, achieving above 98.2% for mean accuracy. Moreover, the PINN-GCN framework can produce high-resolution predictions, even with low-resolution field training data. Furthermore, the PINN-GCN prediction speed was approximately 1000 times faster than that of the numerical simulations. Thus, the proposed model can rapidly predict high-resolution flow fields using a physics-informed, grid- and geometry-adaptive, data-driven model.