Improved Self-Adaptive Physics-Informed Neural Network with SHAP-Based Interpretability for Temperature Field Simulation in Electroslag Remelting

The traditional electroslag remelting (ESR) process mainly relies on mechanism model analysis to obtain the internal temperature distribution, but this method has high data acquisition costs, huge data volume, and takes up a lot of computing resources. For this reason, this paper proposes a method that embeds the self-encoder and the finite volume method (FVM) into the self-adaptive physics-informed neural network (SA-PINN) framework to quickly predict the high-precision temperature field of the ESR process. The model of the end-point temperature of the ESR process is completed by minimizing the loss function composed of data errors, physical equation errors and boundary condition errors. Among them, the self-encoder compresses the temperature field data to reduce the amount of data processed by the full connection layer, and the finite volume method is used to replace the automatic differential technology (Autodiff) to improve the physical compliance of the model. In order to further determine the contribution of the key process parameters input to the model to the molten pool depth, the SHAP explanatory analysis framework is used to quantify their contribution to the prediction of the molten pool depth. The results show that the main factors are melting rate and electrode diameter, while the current frequency has a relatively small impact. Based on the 6,561 samples obtained from FVM simulations, the root mean square error of the model was 0.718, the mean absolute error was 0.477, and the coefficient of determination reached 0.9997; whereas the corresponding metrics for the SA-PINN model were 0.926, 0.533, and 0.9895, respectively. The comparison results indicate that the model proposed in this study is capable of achieving high-precision predictions of the ESR temperature field and has the potential to replace traditional numerical methods.