Adaptive graph spatio-temporal synchronization for traffic flow prediction based on NODEs

To tackle the continuity and synchronization in the acquisition of spatio-temporal features for traffic flow prediction, an adaptive graph based on neural ordinary differential equation (AGNODE) model for spatio-temporal synchronized traffic flow prediction was proposed. According to the correlations of semantic and distance in historical traffic flow data, a two-way prior adjacency matrix was defined. An adaptive adjacency matrix with automatically adjustable weights was designed by using dynamic filtering and node embedding. With the prior adjacency matrix and the adaptive adjacency matrix, a fusion layer of the static-dynamic map was established based on the linear weighted fusion, and an adaptive spatio-temporal synchronized graph containing both temporal and spatial dimensions was constructed via the vertex features in the virtual connection layer. The neural ordinary differential equations (NODE) were employed to solve the graph convolutional network (GCN) and then form the graph convolutional NODE (GCNODE). The AGNODE model was constructed by utilizing the time-aligned solution step and double-stacked GCNODE. Using the California freeway public traffic datasets (PeMS04 and PeMS08), combined with indicators such as the mean absolute error (MAE), root mean square error (RMSE), and training and inference time, the AGNODE model was tested and verified. Analysis results show that compared with those of the optimal baseline model of the spatio-temporal graph ordinary differential equation (STGODE), the MAE and RMSE of the AGNODE model in the single-step prediction (5 min) decrease by 3.6% and 2.8% on PeMS04, and by 2.2% and 1.7% on PeMS08, respectively. In the multistep predictions (15, 30, and 60 min), the MAE and RMSE of the AGNODE model decrease by an average of 3.0% and 2.4% on PeMS04, and by an average of 3.6% and 1.2% on PeMS08, respectively. As the network layer increases, the MAE and RMSE of the AGNODE model decrease by 5.3% and 2.6%, while those of the STGODE model decrease by 0.7% and 0.6%, respectively. The training and inference time of the AGNODE model on PeMS04 and PeMS08 decrease by 11.4% and 7.5%, respectively, compared with those of the attention-based spatial-temporal graph convolutional network (ASTGCN). Moreover, the AGNODE model can achieve better prediction accuracy with an additional time of no more than 7.7% compared to STGODE. Therefore, the AGNODE model can exhibit strong capabilities in spatio-temporal modelling and parameter adaptation, accurately predict the short-term traffic flow, and provide reliable flow information and decision basis for traffic participants. © 2025 Chang'an University. All rights reserved.