Temperature fields prediction for the casting process by a conditional diffusion model

Deep learning has achieved great progress in image recognition, segmentation, semantic recognition and game theory. In this study, a latest deep learning model, a conditional diffusion model was adopted as a surrogate model to predict the heat transfer during the casting process instead of numerical simulation. The conditional diffusion model was established and trained with the geometry shapes, initial temperature fields and temperature fields at ti as the condition and random noise sampled from standard normal distribution as the input. The output was the temperature field at ti+1. Therefore, the temperature field at ti+1 can be predicted as the temperature field at t, is known, and the continuous temperature fields of all the time steps can be predicted based on the initial temperature field of an arbitrary 2D geometry. A training set with 302 2D shapes and their simulated temperature fields at different time steps was established. The accuracy for the temperature field for a single time step reaches 97.7%, and that for continuous time steps reaches 69.1% with the main error actually existing in the sand mold. The effect of geometry shape and initial temperature field on the prediction accuracy was investigated, the former achieves better result than the latter because the former can identify casting, mold and chill by different colors in the input images. The diffusion model has proved the potential as a surrogate model for numerical simulation of the casting process.