Modeling natural convection by solving conservative transport equations with physics-informed neural networks

Physics-informed neural networks (PINNs), which integrate governing physical equations directly into neural network architectures, represent a rapidly advancing numerical simulation technique characterized by their mesh-free nature and ability to easily handle inverse problems. Our previous work proposed the PINNforCTE framework for solving conservative-form transport equations, significantly reducing the required training time of the neural network (NN). In this paper, we further optimize the PINNforCTE framework to improve its performance in simulating highly coupled transport equations. Specifically, we simulate natural convection under the Boussinesq assumption across a broad range of Rayleigh numbers, reflecting various levels of coupling between temperature and flow fields. Our results demonstrate that, for low Rayleigh numbers (around 10 3 ), the natural convection can be accurately simulated using the original PINNforCTE. However, as the Rayleigh number increases (up to 10 6 ), modifications of PINNforCTE with adaptive residual points (ARP) and/or Fourier feature network (FFN) become necessary to maintain the simulation accuracy. The modified PINNforCTE frameworks show promise in handling complex transport phenomena, offering improved adaptability and accuracy over traditional PINN approaches.