Physics-informed neural network-based finishing entry temperature correction: A hybrid mechanistic and data-driven approach

Shengyue Zong; Zhao Yang; Jinyan Li; Shengyue Zong; Zhao Yang; Jinyan Li

doi:10.3934/era.2025279

Electronic Research Archive

2025, Volume 33, Issue 10: 6322-6342. doi: 10.3934/era.2025279

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Physics-informed neural network-based finishing entry temperature correction: A hybrid mechanistic and data-driven approach

1.
National Engineering Research Center for Advanced Rolling Technology and Intelligent Manufacturing, University of Science and Technology Beijing, Beijing 100083, China
2.
School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China
3.
Nanjing Steel Group Co., LTD, Nanjing 210035, China

Received: 24 July 2025 Revised: 12 October 2025 Accepted: 15 October 2025 Published: 27 October 2025

In the hot-rolled strip steel production process, the finishing entry temperature (FET) is directly related to the mechanical properties, microstructural uniformity, and surface quality of the steel, while also having a significant impact on energy consumption and carbon emissions. Traditional temperature measurement and prediction methods each have their limitations, such as large measurement errors, high computational complexity, or overfitting issues. To address these challenges, this paper proposes a finishing entry temperature-physics-informed neural network (FET-PINN) method that integrates rough delivery temperature (RDT) data with thermodynamic equations. First, by leveraging the advantage that the temperature in the RDT region more closely approximates the true billet temperature, an initial prediction of the FET was obtained via a FET-PINN model in conjunction with thermodynamic equations. Subsequently, to account for model errors, the fusion weight was calculated using a nonlinear least squares method, and a weighted averaging approach was employed to fuse this predicted value with the temperature computed from instrumentation measurements, thereby achieving a more accurate temperature estimation. Finally, considering the effect of FET on the subsequent rolling force, the paper evaluated the model comprehensively by comparing the predicted rolling force with the actual rolling force using the coefficient of determination ($ R^{2} $), root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) as evaluation metrics. Experimental results demonstrated that the proposed method enhances the accuracy of temperature prediction and provides effective technical support for temperature control in hot rolling processes.
- nonlinear least squares method,
- physics-informed neural network,
- temperature prediction,
- temperature fusion
Citation: Shengyue Zong, Zhao Yang, Jinyan Li. Physics-informed neural network-based finishing entry temperature correction: A hybrid mechanistic and data-driven approach[J]. Electronic Research Archive, 2025, 33(10): 6322-6342. doi: 10.3934/era.2025279

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Abstract

In the hot-rolled strip steel production process, the finishing entry temperature (FET) is directly related to the mechanical properties, microstructural uniformity, and surface quality of the steel, while also having a significant impact on energy consumption and carbon emissions. Traditional temperature measurement and prediction methods each have their limitations, such as large measurement errors, high computational complexity, or overfitting issues. To address these challenges, this paper proposes a finishing entry temperature-physics-informed neural network (FET-PINN) method that integrates rough delivery temperature (RDT) data with thermodynamic equations. First, by leveraging the advantage that the temperature in the RDT region more closely approximates the true billet temperature, an initial prediction of the FET was obtained via a FET-PINN model in conjunction with thermodynamic equations. Subsequently, to account for model errors, the fusion weight was calculated using a nonlinear least squares method, and a weighted averaging approach was employed to fuse this predicted value with the temperature computed from instrumentation measurements, thereby achieving a more accurate temperature estimation. Finally, considering the effect of FET on the subsequent rolling force, the paper evaluated the model comprehensively by comparing the predicted rolling force with the actual rolling force using the coefficient of determination ($ R^{2} $), root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) as evaluation metrics. Experimental results demonstrated that the proposed method enhances the accuracy of temperature prediction and provides effective technical support for temperature control in hot rolling processes.

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