  High-performance traffic flow prediction model designing, a core technology
of Intelligent Transportation System, is a long-standing but still challenging
task for industrial and academic communities. The lack of integration between
physical principles and data-driven models is an important reason for limiting
the development of this field. In the literature, physics-based methods can
usually provide a clear interpretation of the dynamic process of traffic flow
systems but are with limited accuracy, while data-driven methods, especially
deep learning with black-box structures, can achieve improved performance but
can not be fully trusted due to lack of a reasonable physical basis. To bridge
the gap between purely data-driven and physics-driven approaches, we propose a
physics-guided deep learning model named Spatio-Temporal Differential Equation
Network (STDEN), which casts the physical mechanism of traffic flow dynamics
into a deep neural network framework. Specifically, we assume the traffic flow
on road networks is driven by a latent potential energy field (like water flows
are driven by the gravity field), and model the spatio-temporal dynamic process
of the potential energy field as a differential equation network. STDEN absorbs
both the performance advantage of data-driven models and the interpretability
of physics-based models, so is named a physics-guided prediction model.
Experiments on three real-world traffic datasets in Beijing show that our model
outperforms state-of-the-art baselines by a significant margin. A case study
further verifies that STDEN can capture the mechanism of urban traffic and
generate accurate predictions with physical meaning. The proposed framework of
differential equation network modeling may also cast light on other similar
applications.
