  As a core technology of Intelligent Transportation System, traffic flow
prediction has a wide range of applications. The fundamental challenge in
traffic flow prediction is to effectively model the complex spatial-temporal
dependencies in traffic data. Spatial-temporal Graph Neural Network (GNN)
models have emerged as one of the most promising methods to solve this problem.
However, GNN-based models have three major limitations for traffic prediction:
i) Most methods model spatial dependencies in a static manner, which limits the
ability to learn dynamic urban traffic patterns; ii) Most methods only consider
short-range spatial information and are unable to capture long-range spatial
dependencies; iii) These methods ignore the fact that the propagation of
traffic conditions between locations has a time delay in traffic systems. To
this end, we propose a novel Propagation Delay-aware dynamic long-range
transFormer, namely PDFormer, for accurate traffic flow prediction.
Specifically, we design a spatial self-attention module to capture the dynamic
spatial dependencies. Then, two graph masking matrices are introduced to
highlight spatial dependencies from short- and long-range views. Moreover, a
traffic delay-aware feature transformation module is proposed to empower
PDFormer with the capability of explicitly modeling the time delay of spatial
information propagation. Extensive experimental results on six real-world
public traffic datasets show that our method can not only achieve
state-of-the-art performance but also exhibit competitive computational
efficiency. Moreover, we visualize the learned spatial-temporal attention map
to make our model highly interpretable.
