Physics-guided Active Sample Reweighting for Urban Flow Prediction

Urban flow prediction is a spatio-temporal modelling 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 (e.g., uncalibrated traffic sensors). 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 (e.g., one record per 30 minutes) in many transportation services, the instantaneous dynamics of urban flows can hardly be captured, rendering differential equation-based continuous modelling a loose fit for this setting. To overcome the challenges, we develop a discretized physics-guided network (PN), and propose a data-aware framework <u>P</u>hysics-<u>g</u>uided <u>A</u>ctive <u>S</u>ample <u>R</u>eweighting (P-GASR) to enhance PN. Technically, P-GASR incorporates an active sample reweighting pipeline, which not only minimizes the model uncertainty of PN to enhance robustness, but also prioritizes data samples that exhibit higher physical compliance to reinforce their contribution to PN training. Experimental results in four real-world datasets demonstrate that our method achieves state-of-the-art performance with a demonstrable improvement in robustness. The code is released at https://github.com/WeiJiang01/P-GASR.