  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
