An asymptotic approach for temperature field prediction in process equipment based on generative and graph neural network models

Thermal processing is commonly used in process manufacturing, where temperature is a critical factor dictating material phase transformations and microstructural evolution. Accurate and real-time calculation of the temperature field is essential for guiding certain production decisions. However, traditional offline methods involving numerical analysis are limited in their ability to support real-time process monitoring due to the complexity of the production environment. Additionally, temperature field data in production are often characterized by small sample sizes, significant discrepancies between input and output data dimensions, and complex temperature distribution patterns. Under these conditions, existing surrogate models typically struggle to achieve satisfactory accuracy. To address these challenges, this paper proposes a novel generative model for generating temperature data samples based on an encoding-decoding framework, which effectively balances dimensional discrepancies and facilitates the expansion of temperature data. Building on this, an asymptotic temperature field graph data modeling approach is introduced, which focuses on addressing dimensional differences and capturing spatial relationships among temperature points. A graph neural network is utilized to perform directional aggregation and feature updates based on the spatial correlations of temperature points, leading to an asymptotic solution architecture that enables accurate resolution of the temperature field. Finally, to enhance the model's adaptability to new data, we introduce transfer learning strategies—including error tracing and migration techniques—which significantly improve model performance in dynamic production environments.