A Data-Driven Reduced-Order Model for Rotary Kiln Temperature Field Prediction Using Autoencoder and TabPFN

The accurate reconstruction of the internal temperature field in rotary kilns is critical for optimizing the clinker calcination process and ensuring energy efficiency. In this study, a rapid and high-fidelity surrogate modeling framework is proposed, utilizing snapshot ensembles generated by full-order Computational Fluid Dynamics (CFD) simulations to reconstruct the temperature field of the axial center section. The framework incorporates a symmetric Autoencoder (AE) coupled with a TabPFN network as its core components. Capitalizing on the kiln’s strong axial symmetry, this reduction–regression system efficiently maps the high-dimensional nonlinear thermodynamic topology of the central section into a compact low-dimensional latent manifold via AE, while utilizing TabPFN to establish a robust mapping between operating boundary conditions and these latent features. By leveraging the In-Context Learning (ICL) mechanism for prior-data fitting, TabPFN effectively overcomes the data scarcity inherent in high-cost CFD sampling. Predictive results demonstrate that the model achieves a coefficient of determination (R2) of 0.897 for latent feature regression, outperforming traditional algorithms by 6.53%. In terms of field reconstruction on the test set, the model yields an average temperature error of 15.31 K. Notably, 93.83% of the nodal errors are confined within a narrow range of 0–50 K, and the reconstructed distributions exhibit high consistency with the CFD benchmarks. Furthermore, compared to the hours required for full-scale simulations, the inference time is reduced to 0.45 s, representing a speedup of four orders of magnitude. Consequently, the predictive system demonstrates excellent accuracy and efficiency, serving as an effective substitute for traditional models to realize online monitoring and intelligent optimization.