CFormer-PINN: A physics-informed transformer network with adaptive gating for end-point carbon prediction in BOF steelmaking

Accurate end-point carbon prediction in basic oxygen furnace (BOF) steelmaking is critical. This article addresses two key challenges. Mechanism models suffer from difficult online identification of kinetic parameters. Data-driven models lack physical constraints and suffer from difficult accurate identification of critical parameters. To solve these problems, this article proposes CFormer-PINN (carbon transformer physics-informed neural network). A mechanism equation for the post-blowing stage is established and embedded as a physical constraint via physics-informed neural network. A Transformer module replaces traditional recurrent networks to enhance temporal feature extraction. A gating-based dual-branch adaptive fusion method is designed with a multi-constraint collaborative loss function. These enable automatic learning of weights between physical and data-driven branches. Experiments use 800 heats of production data from a domestic steel plant. The dataset is divided into 650 heats for training, 75 for validation, and 75 for testing. Results show that CFormer-PINN achieves hit rates of 46.67%, 82.67%, and 97.33% within ± 0.005%, ± 0.01%, and ± 0.015%, respectively. The mean absolute error is 0.00553. Compared with the pure physics model, the hit rate within ± 0.01% is improved by 17.34 percentage points. Compared with multilayer perceptron-based physics-informed neural network, the improvement is 12.71 percentage points. The proposed model significantly enhances prediction accuracy and physical interpretability for carbon content prediction in the post-blowing stage.