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 this https URL

本文提出了一种新颖的基于图的多 - ODE 神经网络（GRAM-ODE）架构，通过捕捉复杂的局部和全局动态时空依赖关系的不同视图来学习更好的表示，并在其中间层添加了共享权重和发散性约束等技术以进一步改善面向预测任务的通信。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明显的优越性，并且不同组件对整体性能的贡献。

基于图结构的多元素 ODE 神经网络用于时空交通预测

Graph-based Multi-ODE Neural Networks for Spatio-Temporal Traffic  Forecasting

We introduce a rigorous framework for stochastic cell transmission models for
general traffic networks. The performance of traffic systems is evaluated based
on preference functionals and acceptable designs. The numerical implementation
combines simulation, Gaussian process regression, and a stochastic exploration
procedure. The approach is illustrated in two case studies.

本文提出了一种基于偏好函数和可接受设计的随机单元传输模型的严格框架，并进行了数字实现，其中集成了仿真、高斯过程回归和随机探索程序。该方法在两个案例研究中得以验证。