Non-Fourier Heat Conduction based on Self-Adaptive Weight Physics-Informed Neural Networks

This paper establishes the non-Fourier heat conduction model to describe the heat transfer process of mono-crystalline silicon under the condition of unstable thermal field and thermal shock in the Czochralski method. A novel differential equations solver called Physics-Informed Neural Networks (PINN) algorithm was introduced. Compared with finite element method (FEM), this method has some advantages like no grid requirement and easily solving. In order to deal with the unbalance of constraint condition and speed up the convergence, we propose a novel method called Self-Adaptive Weight Physics-Informed Neural Networks(SWPINN). The comparison of the experimental results of SWPINN and COMSOL verifies the effectiveness of SWPINN. By modifying the parameter of non-Fourier heat conduction model, this paper obtains the temperature distribution under different heat relaxation times. Finally, comparison between SWPINN and PINN shows that the proposed method has faster convergence speed and higher accuracy.