Physics-guided Active Sample Reweighting for Urban Flow Prediction

TL;DR

This work addresses the mismatch between data and physics in urban flow prediction by introducing Physics-guided Active Sample Reweighting (P-GASR). It combines a discretized physics-guided network (PN) that respects a discrete urban flow continuity equation with an active reweighting policy that jointly accounts for model uncertainty and physical consistency to downweight noisy or nonconforming samples. Through extensive experiments on four real-world taxi and bike-flow datasets, P-GASR achieves state-of-the-art performance and demonstrates robustness to data quality variations, outperforming both purely data-driven baselines and continuous-physics models. The approach advances practical urban flow forecasting by hardening PGML methods against data imperfections while preserving interpretability and physics-informed structure.

Abstract

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.

Figures (8)

• Figure 1: A toy example illustrates that urban energy density changes over time in accordance with conservation law when subject to physical consistency, whereas physical inconsistency results in a violation of the conservation law. The arrows represent the direction of urban energy flux flow, the thickness of the edges represents the magnitude of the flux, and the size of the nodes reflects the urban energy density.
• Figure 2: Influence of different noise levels on physics-guided network on four passenger demand prediction datasets (see experimental settings in Sec. \ref{['sec:experiment_set']} and \ref{['sec:noise_influence']}).
• Figure 4: An overview of the P-GASR framework. Our P-GASR consists of two important parts: physics-guided network and active reweighting policy. In the proposed active reweighting policy, we design two components to compute the sample weights considering both data-driven and physics-guided aspects. We utilize Monte Carlo-dropout to measure model uncertainty, where $s^2(\tilde{\bm{x}},\bm{\Theta})$ represents the variance of $K$ prediction rounds. On the other hand, we use L2 distance between urban flow aggregation $\bm{A}\tilde{\bm{x}}$ and future prediction $\tilde{y}_{\text{pred}}$ to measure physical consistency based on the conservation law in discrete form.
• Figure 5: Influence of different noise levels to P-GASR and PN.
• Figure 6: Performance comparison of ablation study with the variants of P-GASR.