Network-wide fine-grained passenger loading prediction via dynamic relational spatiotemporal deep graph neural networks

Accurate short-term prediction of onboard passenger loading is essential for enhancing public transport efficiency, passenger comfort, and operational resilience. However, existing models are mainly restricted to station-based passenger flow prediction, and they often struggle with the spatiotemporal complexity of multi-line systems and the “incomplete data” problem caused by sensor failures or canceled services. This study proposes the Dynamic Relational Graph Convolutional Recurrent Neural Network (DRGCRNN) framework designed for edge-level, fine-grained passenger load forecasting. The framework explicitly models hierarchical dependencies through three relational graphs: a static physical layout, a probabilistic operational information graph, and a dynamic loading graph. To address data incompleteness, a Positive-Unlabeled learning module is integrated to infer reliability-adjusted service-execution probabilities. Furthermore, the network is projected into an adjoint “line graph” to capture inter-line and edge-to-edge dependencies. Validated using real-time vehicle location and passenger counting data from the Helsinki commuter rail network, the DRGCRNN achieves competitive overall performance and shows clear advantages during peak periods, where passenger volumes and cross-line interactions are more pronounced. The results demonstrate that the model effectively captures and predicts the loading patterns of high-frequency transit, providing a scalable template for service-specific real-time crowding monitoring and operational decision support. Our code is publicly available.