Research on the thermal-fluid coupling in the growth process of Czochralski silicon single crystals based on an improved physics-informed neural network

To address the limitations of conventional numerical methods in modeling complex thermal-fluid coupling during Czochralski (CZ) silicon single crystal growth process, this paper proposes a physics-informed neural network (PINN) incorporating enhanced spatial information and adaptive loss balancing (SI-LB-PINN). This network enhances the capability to capture multi-physics field characteristics by incorporating spatial information while dynamically balancing the contributions of different loss terms through an adaptive weighting algorithm, effectively improving both training stability and predictive accuracy. This paper takes natural convection in a square cavity as the subject, and employs the SI-LB-PINN to predict the fluid temperature and velocity distribution features. A comparative analysis is conducted against several enhanced PINN variants to evaluate the effectiveness of the proposed SI-LB-PINN. Following this validation, the method is applied to address the thermal-fluid coupling problem in the CZ silicon single crystal growth process, yielding accurate velocity and temperature distributions of the silicon melt under multi-physics field coupling conditions. Experimental results demonstrate that, compared to other networks, the SI-LB-PINN proposed in this paper can more accurately represent the complex physical characteristics of thermal-fluid coupling and accurately predict the flow velocity and temperature field distribution of the silicon melt.