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.
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