Pi-TabNet: An explainable physics-informed deep learning method for flatness prediction in cold-rolled copper strips

Abstract

Flatness is a critical quality indicator for high-end cold-rolled strip products. In industrial applications, flatness is automatically measured and controlled through flatness measurement and control systems. Traditional mechanistic models for flatness prediction face challenges, including low accuracy, lengthy development cycles, and slow computational speeds. Although deep learning-based intelligent models show potential, their industrial adoption remains limited due to poor explainability, insufficient incorporation of physics-informed knowledge from the rolling domain, and low-quality training data. Furthermore, flatness prediction for cold-rolled copper strips remains an underexplored research area. To address these challenges, this study proposes an explainable, physics-informed deep learning method for flatness prediction at the exit stage of cold-rolled copper strips. Using industrial big data, actual operating conditions, and data mining techniques, two flatness datasets were constructed for cold-rolled copper strips under representative industrial scenarios. Guided by prior physical knowledge from the rolling domain, a novel deep neural network architecture, Physics-informed TabNet (Pi-TabNet), was developed. The training process incorporates physical constraints, ensuring that flatness predictions comply with physical laws, which improves the model's explainability and robustness. The results on the test set indicate that the proposed method achieves higher prediction accuracy than other classical algorithms and demonstrates strong generalization performance. Furthermore, transfer learning experiments indicate that the proposed physics-informed model possesses strong feature extraction capabilities and adapts well to varying data distributions across different scenarios. Additionally, the SHapley Additive exPlanations (SHAP) method, an explainable artificial intelligence (XAI) technique, was employed to elucidate the model's decision-making process, which improves the transparency and reliability of the predictions. Finally, a physical consistency analysis method based on Legendre basis functions is proposed to systematically verify the model's physical consistency and interpretability under perturbations of key process parameters.