There is a recent surge in the development of spatio-temporal forecasting models in the transportation domain. Long-range traffic forecasting, however, remains a challenging task due to the intricate and extensive spatio-temporal correlations observed in traffic networks. Current works primarily rely on road networks with graph structures and learn representations using graph neural networks (GNNs), but this approach suffers from over-smoothing problem in deep architectures. To tackle this problem, recent methods introduced the combination of GNNs with residual connections or neural ordinary differential equations (ODE). However, current graph ODE models face two key limitations in feature extraction: (1) they lean towards global temporal patterns, overlooking local patterns that are important for unexpected events; and (2) they lack dynamic semantic edges in their architectural design. In this paper, we propose a novel architecture called Graph-based Multi-ODE Neural Networks (GRAM-ODE) which is designed with multiple connective ODE-GNN modules to learn better representations by capturing different views of complex local and global dynamic spatio-temporal dependencies. We also add some techniques like shared weights and divergence constraints into the intermediate layers of distinct ODE-GNN modules to further improve their communication towards the forecasting task. Our extensive set of experiments conducted on six real-world datasets demonstrate the superior performance of GRAM-ODE compared with state-of-the-art baselines as well as the contribution of different components to the overall performance. The code is available at https://github.com/zbliu98/GRAM-ODE

翻译：近年来，交通领域的时空预测模型开发呈激增态势。然而，由于交通网络中观测到的复杂且广泛的时空相关性，长期交通预测仍是一项具有挑战性的任务。当前研究主要依赖具有图结构的道路网络，并使用图神经网络学习表示，但这种方法在深度架构中存在过度平滑问题。为解决该问题，近期方法引入了图神经网络与残差连接或神经常微分方程的结合。然而，当前的图ODE模型在特征提取方面面临两个关键限制：（1）它们倾向于全局时间模式，忽视了对于突发事件至关重要的局部模式；（2）其架构设计中缺乏动态语义边。在本文中，我们提出了一种新颖架构——基于图的多ODE神经网络，该架构设计有多个连接性的ODE-GNN模块，通过捕获复杂局部和全局动态时空依赖的不同视图来学习更好的表示。我们还在不同ODE-GNN模块的中间层添加了如共享权重和散度约束等技术，以进一步改善它们在预测任务中的通信。我们在六个真实数据集上进行的广泛实验表明，GRAM-ODE相比最先进的基线方法具有优越性能，同时验证了不同组件对整体性能的贡献。代码可在 https://github.com/zbliu98/GRAM-ODE 获取。