A PIKAN-based model for the prediction of the temperature fields of castings

In the casting process, solving various physical quantities centered on the temperature field through numerical simulation is very helpful for optimizing the process. The rapid development of deep learning technology offers potential for industrial applications and can represent a new simulation methodology. This study proposes a PIKAN model that groups spatiotemporal parameters and inputs them through an MLP model. During the training process, this study used a loss function that combines physical loss and data loss, and identified the optimal weight parameters through Bayesian optimization. Pre-training with multiple casting geometries as labels has improved the efficiency of model prediction. With an absolute error of 10 K as the critical value, the average temperature error of this study is 5.62 K, and the average accuracy reaches 88.74%. This study predicts the evolution of the two-dimensional temperature field during the casting solidification process using deep learning, supporting the application of new technologies in engineering.