An Optimization-Driven Fuzzy Transformer–Deep Belief Network for PM_2.5 Air Pollution Prediction: A Spatio-Temporal Framework Based on Aerosol Optical Depth

Forecasting fine particulate matter with a diameter of 2.5 μm (PM_2.5) is critically important due to its adverse effects on human health and environmental sustainability. Although ground-based monitoring stations provide accurate measurements, their limited spatial coverage restricts large-scale PM_2.5 assessment, especially in complex urban regions. Consequently, aerosol optical depth (AOD) derived from satellite imagery, combined with advanced deep learning (DL) techniques, has emerged as an effective alternative by offering wide spatial coverage and rich spatio-temporal information. This paper proposed an optimization-driven fuzzy transformer–deep belief network (ODFT-DBN) for accurate PM_2.5 air pollution prediction. The proposed framework integrates a fuzzy inference module to model uncertainty and nonlinear environmental relationships, a transformer encoder to capture long-range spatio-temporal dependencies, and a DBN to extract hierarchical features and improve prediction robustness. In addition, a novel multi-objective gray wolf optimizer (NMOGWO) is employed to jointly optimize the model hyper-parameters and fuzzy membership functions. The proposed approach is implemented for the city of Tehran, Iran, using meteorological variables, topographical features, ground-based PM_2.5 measurements, and satellite-derived AOD data. The ODFT-DBN model is compared with several benchmark methods, including bidirectional encoder representations from transformers (BERT), transformer, long short-term memory (LSTM), gated recurrent unit (GRU), convolutional neural network (CNN), DBN, and extreme gradient boosting (XGBoost). Experimental results demonstrate that the proposed framework achieves superior predictive performance, attaining an R² value of 0.94 and root mean square error (RMSE) of 0.8 μg/m³. Scatter plot analyses indicate a strong agreement between predicted and observed PM_2.5 values, while the proposed model exhibits low variance, stable convergence behavior, and acceptable computational time. Overall, the results confirm the effectiveness, robustness, and practical applicability of the proposed ODFT-DBN framework for spatio-temporal PM_2.5 forecasting.