A Hybrid Soot-MixFormer-Based Reconstruction Model for 2D Soot Spatial Distribution Inversion

Accurate measurement of the 2D soot spatial distribution is vital for optimizing combustion efficiency and reducing pollutant emissions. While 1D laser extinction (LE) is robust and cost-effective, it provides only line-of-sight integrated information, lacking the spatial resolution required to resolve complex soot topologies. We propose Soot-MixFormer, a hybrid deep learning model designed for the high-fidelity inversion of 2D soot distributions from 1D extinction data. The architecture integrates CNN-based local feature extraction with Transformer-based global dependency modeling. Key innovations include a dynamic decoupled generation head and a Dual-Axial Gated Refinement (DAGR) module coupled with a physical hard constraint layer to ensure mass conservation and physical consistency. Experimental results demonstrate that Soot-MixFormer significantly outperforms baseline MLP and CNN models, achieving a Structural Similarity Index (SSIM) of 0.800 and a Pearson Correlation Coefficient (PCC) of 0.915, and a highly suppressed Root Mean Square Error (RMSE) representing less than 10% relative error in high-concentration zones. Furthermore, the model exhibits exceptional robustness, maintaining a cosine similarity above 0.72 even under 10% simulated measurement noise. The model is highly efficient, with only 0.97 M parameters and a real-time inference speed of ~246 FPS. This study provides a novel, low-cost diagnostic paradigm for real-time, high-accuracy monitoring of soot fields in industrial combustion environments, effectively bridging the gap between simple 1D sensing and complex 2D spatial reconstruction.