Boosting PM2.5 short-term prediction by coupling graph attention and koopman networks

Accurately predicting PM2.5 concentrations remains a major challenge due to the complex and nonlinear nature of its formation and transport processes. Traditional models often struggle to capture the spatiotemporal dynamics of PM2.5, particularly under varying meteorological conditions. In recent years, Koopman operator theory has attracted increasing attention for its ability to transform nonlinear systems into linear representations, thereby enhancing model interpretability and stability. However, most existing Koopman models primarily focus on temporal dynamics and overlook the spatial correlations. To address this limitation, we propose a novel framework called Graph Attention Physics-Constrained Learning (GAPCL). This method combines Graph Attention Networks—designed to model spatial dependencies between PM₂.₅ monitoring stations—with the Physics-Constrained Learning framework grounded in Koopman theory. The model employs an attention mechanism to dynamically weight PM2.5 monitoring stations, uncover spatial relationships, and integrates graph topology with Koopman eigenfunctions to represent the spatiotemporal evolution of complex nonlinear dynamical systems. The effectiveness of GAPCL was validated using hourly data from 2019 to 2021 in the Beijing-Tianjin-Hebei region. The results demonstrated that the model achieved superior prediction accuracy, particularly for short-term forecasts. Compared to the Spatial Physics Constrained Learning (SPCL), GAPCL improved the RMSE, MAE, IA, and r by an average of 12.07%, 11.47%, 11.16%, and 11.11%, respectively. Additionally, the mean RMSE of GAPCL was 3.26% lower than the next-best SPCL and 26.64% lower than the worst-performing Long Short-Term Memory Network. The GAPCL model significantly improves outlier prediction accuracy by dynamically weighting PM2.5 stations to better capture spatial dependencies.