  Urban flow prediction is a spatio-temporal modeling task that estimates the
throughput of transportation services like buses, taxis, and ride-sharing,
where data-driven models have become the most popular solution in the past
decade. Meanwhile, the implicitly learned mapping between historical
observations to the prediction targets tend to over-simplify the dynamics of
real-world urban flows, leading to suboptimal predictions. Some recent
spatio-temporal prediction solutions bring remedies with the notion of
physics-guided machine learning (PGML), which describes spatio-temporal data
with nuanced and principled physics laws, thus enhancing both the prediction
accuracy and interpretability. However, these spatio-temporal PGML methods are
built upon a strong assumption that the observed data fully conforms to the
differential equations that define the physical system, which can quickly
become ill-posed in urban flow prediction tasks. The observed urban flow data,
especially when sliced into time-dependent snapshots to facilitate predictions,
is typically incomplete and sparse, and prone to inherent noise incurred in the
collection process. As a result, such physical inconsistency between the data
and PGML model significantly limits the predictive power and robustness of the
solution. Moreover, due to the interval-based predictions and intermittent
nature of data filing in many transportation services, the instantaneous
dynamics of urban flows can hardly be captured, rendering differential
equation-based continuous modeling a loose fit for this setting. To overcome
the challenges, we develop a discretized physics-guided network (PN), and
propose a data-aware framework Physics-guided Active Sample Reweighting
(P-GASR) to enhance PN. Experimental results in four real-world datasets
demonstrate that our method achieves state-of-the-art performance with a
demonstrable improvement in robustness.
