A Bayesian Physics-Informed Neural Network for End-Point Carbon Prediction and Risk-Aware Control in Electric Arc Furnaces

The precise prediction of end-point carbon content in electric arc furnace (EAF) steelmaking is crucial for maintaining liquid steel quality and optimizing refining costs; however, traditional data-driven models are inadequate due to the strong non-linearity and transient dynamics of the EAF process. This paper presents a novel framework integrating a Bayesian Physics-Informed Neural Network (BPINN), which enhances end-point carbon prediction while addressing the inherent uncertainties of the EAF smelting process. By embedding the carbon oxidation mass conservation equation as a soft constraint within a variational inference framework, this approach effectively incorporates metallurgical physical priors into statistical inference. Extensive validation conducted on 9673 production heats from a 130 t direct-current EAF reveals that the BPINN significantly reduces the mean absolute error to 0.0072 pct, achieving a hit rate of 91.7 pct. Furthermore, the model demonstrates robustness under extreme out-of-distribution scenarios, such as deep decarburization stages and sudden scrap composition changes, by enforcing physical constraints that mitigate performance degradation. Additionally, a risk-aware hierarchical control system is established to classify control instructions based on prediction intervals. This study provides a reliable pathway from deterministic numerical prediction to risk-aware control in uncertain metallurgical processes.