Simulation of thermal-fluid coupling in silicon single crystal growth based on gradient normalized physics-informed neural network

The thermal-fluid coupling phenomenon of silicon melt is significant in the growth process of silicon single crystals. Complex convection affects the temperature and concentration distribution of the silicon melt. Therefore, establishing and solving the thermal-fluid coupling model of silicon melts is crucial to optimizing the crystal growth process and improving crystal quality. Traditional numerical simulation methods have limitations in regard to optimization, control, and real-time monitoring. Physics-Informed Neural Network (PINN) does not require model discretization, after training, it can make predictions quickly, showing potential for industrial applications. However, when solving practical industrial coupling models, PINN often struggles to converge due to large parameter values and significant gaps between solution variables. Moreover, solving the thermal-fluid coupling model with PINN can be treated as a multitask problem, where the gradients of different equations interfere with each other, leading to gradient confusion, slow convergence, or even divergence. Therefore, this paper proposes a gradient normalized PINN (GNPINN) for solving the thermal-fluid coupling model of silicon melt. GNPINN balances the contribution of each task, ensuring a more equitable training speed between different tasks to stabilize the training process of the coupling model. This paper considers the thermal-fluid coupling model of silicon melt under different rotation conditions. GNPINN can accurately and comprehensively capture the complex temperature, velocity, and pressure distribution of silicon melt compared with other methods. Additionally, the experimental results uncover the flow and heat transfer properties of silicon melt, validating the effectiveness and industrial applicability of GNPINN.