Continuously Evolving Graph Neural Controlled Differential Equations for Traffic Forecasting

TL;DR

This paper addresses traffic forecasting by modeling both continuous temporal dynamics and spatial dependencies that evolve over time. It introduces CE GNCDE, coupling a continuously evolving graph generator (CEGG) with a graph neural controlled differential equation (GNCDE) framework to learn a time-varying adjacency ${\bm{A}(t)}$ and propagate information via NCDEs. Key contributions include (i) a NCDE-based CEGG that blends dynamic adjacency with a stable static graph ${\bm{A}_{\rm{S}}}$, and (ii) a GNCDE with geographic and semantic masks to capture local and global dependencies, all solved in one augmented ODE for efficiency. Experiments on six PeMS datasets demonstrate state-of-the-art accuracy with meaningful ablations and case studies, highlighting the practical impact for ITS and smart city traffic management.

Abstract

As a crucial technique for developing a smart city, traffic forecasting has become a popular research focus in academic and industrial communities for decades. This task is highly challenging due to complex and dynamic spatial-temporal dependencies in traffic networks. Existing works ignore continuous temporal dependencies and spatial dependencies evolving over time. In this paper, we propose Continuously Evolving Graph Neural Controlled Differential Equations (CEGNCDE) to capture continuous temporal dependencies and spatial dependencies over time simultaneously. Specifically, a continuously evolving graph generator (CEGG) based on NCDE is introduced to generate the spatial dependencies graph that continuously evolves over time from discrete historical observations. Then, a graph neural controlled differential equations (GNCDE) framework is introduced to capture continuous temporal dependencies and spatial dependencies over time simultaneously. Extensive experiments demonstrate that CEGNCDE outperforms the SOTA methods by average 2.34% relative MAE reduction, 0.97% relative RMSE reduction, and 3.17% relative MAPE reduction.

Figures (4)

• Figure 1: Overall Framework of CEGNCDE.
• Figure 2: Illustration of Path.
• Figure 3: Attention Module of CEGG.
• Figure 4: Case Study of CEG.