Traffic forecasting using spatio-temporal dynamics and attention with graph attention PDEs

Accurate traffic forecasting is vital for optimizing intelligent transportation systems (ITS), yet existing models often struggle to capture the complex spatio-temporal patterns of urban traffic. We present GAPDE (Graph Attention Partial Differential Equation), a novel framework that integrates Partial Differential Equations (PDEs), Graph Convolutional Networks (GCNs), and advanced attention mechanisms. GAPDE enables continuous-time spatio-temporal modeling and dynamically prioritizes critical features through attention-driven traffic forecasting. Experiments on benchmark datasets, including PEMS-BAY, METR-LA, and various PeMS collections (PeMS03, PeMS04, PeMS07, PeMS08, PeMSD7M, and PeMSD7L), demonstrate GAPDE's superior performance over state-of-the-art models such as RGDAN, SGODE-RNN, and STD-MAE. GAPDE achieves up to 9.2 percent lower RMSE and 10.4 percent lower MAE, outperforming baselines in both short- and long-term prediction tasks. It demonstrates strong robustness to missing data, high scalability for large-scale networks, and enhanced interpretability through spatial and temporal attention visualizations. Comprehensive comparative evaluations and an in-depth ablation study further validate the effectiveness of GAPDE's components, including the GPDE block and spatio-temporal attention mechanisms. By combining PDEs, GCNs, and attention mechanisms in a scalable and efficient design, GAPDE offers a robust solution for real-time traffic forecasting in complex urban environments.