Learning Weekly Urban Evolution: Delay-Coupled Neural Dynamics for Extremely Long-Horizon Spatiotemporal Forecasting

Understanding how cities evolve over long horizons is essential for capacity allocation, operational scheduling, and emergency management. As horizons extend from hours to days, city-wide traffic states evolve continuously across temporal phases, giving rise to complex spatiotemporal dynamics. Our analysis of real-world traffic data identifies three interrelated challenges: delayed interactions among nodes and their temporal accumulation, changing dependencies across phases and days, and the joint representation of long-term periodicity and local peak and trough variations. To address these challenges, we propose Delay-Coupled Neural Dynamics (DeCoDy), a graph dynamics framework with time delays for modeling extremely long-horizon urban evolution. DeCoDy addresses them through Multi-Delay Interaction and Accumulation, Phase Evolution and Adaptive Coupling, and Global and Local Residual Representation, while generating continuous future trajectories with a constrained full-horizon response solver. We evaluate DeCoDy on four real-world urban traffic datasets with horizons from 8 hours to 7 days. DeCoDy achieves the lowest MAE in 14 of 16 dataset–horizon settings and the lowest RMSE on all four datasets for 7-day forecasting, demonstrating its effectiveness in modeling extremely long-horizon urban evolution.