Simulation of thermoelastic coupling in silicon single crystal growth based on alternate two-stage physics-informed neural network

Abstract

This paper proposes a alternate physics-informed neural network (PINN) with a two-stage training strategy to solve the thermoelastic coupling in the growth of Czochralski silicon single crystal. Particularly, neural networks with a two-stage training strategy are established for solving partial differential equations in the thermoelastic coupling model. At present, PINN still faces challenges in solving coupling models. Especially for the imbalance between and within equations in the coupling model. To solve this problem, this paper splits the model into two independent systems with their coupling term exchanged in the alternating iteration. Then, the imbalance inside a single solution of the coupling model is solved by the proposed two-stage training strategy, and the imbalance between solutions is avoided by alternative iterations. Experimental results show that the proposed alternate two-stage PINN (ATPINN) can accurately simulate the temperature and displacement in the thermoelastic coupling model. Compared with the finite element results, the error of temperature prediction and displacement prediction is acceptable. The numerical results demonstrate the feasibility and performance of the ATPINN. Furthermore, ATPINN can be extended to any type of coupling model, especially for coupling models with large differences in the magnitudes of the loss functions. The codes developed in this manuscript are publicy available at https://github.com/callmedrcom/ATPINN.