Fig. 8: TransNet architecture integrating feature engineering, transport operators, and operator splitting for 72-h PM2.5 forecasting.
TransNet framework showing the complete modeling pipeline from feature engineering to forecast generation. The top section shows feature engineering through Variational Mode Decomposition (VMD) applied to PM2.5 time series, producing six intrinsic mode functions (Mode 1: Yearly, Mode 2: Seasonal, Mode 3: Sub-seasonal, Mode 4: Weekly, Mode 5: Turbulent, Mode 6: Residual), and Principal Component Analysis (PCA) applied to pollutant concentrations (6 pollutants coming from in-situ stations), producing three principal components (PC1: Primary Variation, PC2: Secondary Variation, PC3: Tertiary Variation). These processed features combine with meteorological parameters, cyclical temporal encoding, and spatial position encoding to form the input feature set shown in the blue box. The middle section displays TransNet operators including graph construction based on wind speed and wind direction, state embedding containing pollutant, position, and temporal information, and history embedding containing wind, position, and temporal information. The core operator splitting framework implements three sequential physical processes shown in blue boxes: advection (∇·(VU)) for mass conservation, diffusion (K∆(U+1/3)) for spatial smoothing, and reaction (f(U+2/3, Phist, M, θ)) for non-linear interactions. The bottom section shows the output function space where a multilayer perceptron (MLP) projects the evolved features to generate 72-h PM2.5 concentration forecasts.
