A dual-branch boiler water-cooled wall three-dimensional combustion parameter prediction method based on Multi-Head Latent Attention mechanism and Fourier's heat flux density law (M-F dual NET)

This study addresses the inherent ambiguity in inferring internal states of the water-cooled wall region in coal-fired boilers, where limited measurability and heterogeneous operating conditions challenge reliable three-dimensional parameter prediction. We propose a physics-informed 3D prediction framework that synergistically integrates Multi-Head Latent Attention (MLA) with Fourier-law-based thermal constraints. Specifically, Mini-Batch K-Means is first employed to cluster and downsample multi-condition operational data, yielding representative operating points that preserve global regime characteristics while alleviating data redundancy and computational burden. Subsequently, an MLA-empowered M − F Dual NET is developed for multi-scale feature reconstruction. The MLA mechanism selectively captures salient latent representations with negligible overhead, enhancing feature fidelity under complex conditions, whereas a dual-branch collaborative architecture mitigates discrepancies in dimensionality and magnitude across heterogeneous datasets, thereby improving cross-domain coupling and generalization. Furthermore, the heat-conduction partial differential equation derived from Fourier's law is discretized into a finite-difference form and embedded into the loss function, with heat-flux density imposed as a physical constraint to enforce thermodynamic consistency and strengthen interpretability. Comprehensive ablation experiments verify that the progressive incorporation of MLA, dual-branch modeling, and physics-based regularization yields monotonic performance improvements, culminating in an MAE of 0.152 and an R2 of 0.925. The resulting model achieves high-accuracy and physically coherent 3D parameter prediction for boiler water-cooled walls, providing a robust basis for operational optimization and fault diagnosis.