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.

翻译：作为智慧城市的关键技术，交通预测数十年来一直是学术界和工业界的研究热点。由于交通网络中复杂且动态的时空依赖关系，该任务极具挑战性。现有方法忽略了连续的时间依赖关系以及随时间演化的空间依赖关系。本文提出连续演化图神经控制微分方程（CEGNCDE），以同时捕捉随时间变化的连续时间依赖关系和空间依赖关系。具体而言，我们引入基于NCDE的连续演化图生成器（CEGG），从离散历史观测数据中生成随时间连续演化的空间依赖关系图；随后构建图神经控制微分方程（GNCDE）框架，同步捕获连续时间依赖与空间依赖关系。大量实验表明，CEGNCDE较现有最优方法（SOTA）平均降低MAE 2.34%、RMSE 0.97%、MAPE 3.17%。