Real-time prediction of transient temperature fields in continuous casting using a thermophysical-property-embedded conditional Fourier neural operator

Continuous casting is a key metal-processing operation in which transient heat transfer directly governs solidification behavior, microstructure evolution, downstream processing, and final product performance. Real-time and accurate prediction of temperature-field evolution is therefore essential for process monitoring, optimization, and quality control. However, conventional numerical simulations are computationally expensive and are difficult to deploy for real-time prediction, especially under time-varying process disturbances. To address this issue, this study proposes a thermophysical-property-embedded neural operator surrogate framework for long-term transient temperature-field prediction in continuous casting. A dynamic heat-transfer model was first developed for a heating-cooling combined mold by considering temperature-dependent material properties, phase-change-related thermal behavior, interfacial thermal resistance, and convective heat exchange. A tensorized finite-difference parallel solver was then used to generate 2.7 million temperature-field samples under varying process conditions. Based on this dataset, a Conditional Fourier Neural Operator embedded with Thermophysical Properties (CFNO-TP) was trained to model the dynamic evolution operator of the temperature field. The proposed model was validated against high-fidelity numerical solutions under dynamically varying process parameters and showed stable long-term predictive performance. During the 1600 s heating process and the subsequent 315 s continuous-casting process, the maximum absolute temperature errors remained below 4.8 ℃ and 6.7 ℃, respectively. The single-step inference time was less than 0.05 s. These results demonstrate that CFNO-TP provides an efficient surrogate modeling strategy for real-time prediction of transient thermal-state evolution in continuous casting.