A Physics-Guided Transformer–LSTM prediction Model with dynamic feature weighting for NOx emission prediction in CFB boilers

Prediction of nitrogen oxide (NO x ) emissions in coal-fired circulating fluidized bed boilers has achieved significant progress in recent years. However, most existing studies primarily focus on optimizing network architectures while overlooking the role of feature importance heterogeneity. These approaches often assume equal importance among input variables and fail to quantitatively characterize the contributions of operational parameters to the NO x formation process. Moreover, existing approaches lack explicit modeling of physical relationships among variables. To address these issues, this paper proposes a physics-knowledge-embedded feature-weighted temporal end-to-end prediction model, termed PKTL. The framework adaptively quantifies feature dependencies by integrating physics-informed knowledge with temporal positional encoding. In addition, physical knowledge is incorporated into the optimization process through a physics-constrained loss function. Specifically, a novel time–process–function positional encoding (TPFPE) scheme is developed to embed temporal information, process location, and functional prior knowledge into feature representations. Based on this scheme, an improved Transformer encoder is employed to learn feature-wise attention weights, followed by an LSTM network to model temporal dynamics and predict NO x emissions. Experimental results based on real operating data from a CFB unit demonstrate that the PKTL model outperforms baseline models, achieving an R 2 of 0.9568 and reducing RMSE by 18 %. The learned dynamic feature weights further reveal physically meaningful relationships between key operating parameters and NO x formation. Overall, the proposed framework provides an interpretable and effective data-driven approach for NO x emission prediction in complex industrial combustion systems.