Physics-Informed Neural Network Simulation of Thermal Cavity Flow

Abstract Physics-informed neural networks (PINNs) are an emerging technology that can be used both in place of and in conjunction with conventional simulation methods. In this paper, we used PINNs to perform a forward simulation without leveraging known data. Our simulation was of a 2D natural convection-driven cavity using the vorticity-stream function formulation of the Navier-Stokes equations. We used both 2D simulations across the x and z domains for a constant Rayleigh (Ra) number and 3D simulations across the x, z, and Ra domains. This 3D simulation was a test of a PINN’s ability to learn solutions across the parameter space for simulations, which is one potential advantage of PINNs over conventional simulation methods. The simulation results were compared against known solutions at Ra values of 103 , 104 , 105 , and 106. Both the 2D simulations and 3D simulations successfully matched the expected results. For the 2D cases, more training iterations were needed for the model to converge at the higher Ra values of 105 and 106 than at 103 and 104. The 3D case was also able to converge but, as expected, it required more training than any of the 2D cases due to increased dimensionality. These results showed the validity of standard 2D simulations and the feasibility of higher-order parameter space simulations that are not possible using conventional methods. They also showcased the additional computational demand associated with increasing the dimensionality of the learned parameter space.