Air Quality Prediction with Physics-Guided Dual Neural ODEs in Open Systems

TL;DR

Air-DualODE tackles open-system air quality forecasting by integrating physics-based open-system diffusion-advection (via BA-DAE) with data-driven Neural ODE dynamics in a dual-branch framework. A Decaying Temporal Contrastive Learning mechanism aligns the two latent representations, which are fused by a GNN on a geospatial graph to produce accurate pollutant concentration forecasts. Empirical results on Beijing and KnowAir demonstrate state-of-the-art performance and robust ablations reveal complementary strengths of the physics and data-driven components. The method offers interpretability through BA-DAE dynamics (e.g., wind-driven advection and beta maps) and establishes a versatile blueprint for physics-guided dual ODEs in spatiotemporal prediction tasks.

Abstract

Air pollution significantly threatens human health and ecosystems, necessitating effective air quality prediction to inform public policy. Traditional approaches are generally categorized into physics-based and data-driven models. Physics-based models usually struggle with high computational demands and closed-system assumptions, while data-driven models may overlook essential physical dynamics, confusing the capturing of spatiotemporal correlations. Although some physics-guided approaches combine the strengths of both models, they often face a mismatch between explicit physical equations and implicit learned representations. To address these challenges, we propose Air-DualODE, a novel physics-guided approach that integrates dual branches of Neural ODEs for air quality prediction. The first branch applies open-system physical equations to capture spatiotemporal dependencies for learning physics dynamics, while the second branch identifies the dependencies not addressed by the first in a fully data-driven way. These dual representations are temporally aligned and fused to enhance prediction accuracy. Our experimental results demonstrate that Air-DualODE achieves state-of-the-art performance in predicting pollutant concentrations across various spatial scales, thereby offering a promising solution for real-world air quality challenges.

Figures (12)

• Figure 1: The heatmaps show $\text{PM}_\text{2.5}$ concentrations of individual stations at time steps $t$ and $t+1$. In this open system, there are sinks that absorbs pollutants and sources that generates new pollutants, along with pollutants exiting and entering the region's boundary through diffusion and advection.
• Figure 2: The overall framework of Air-DualODE consists of Physics Dynamics, Data-Driven Dynamics, and Dynamics Fusion. $\mathbf{F^P}$ and $\mathbf{F^D}$ represent the ODE functions in Physics Dynamics and Data-Driven Dynamics, respectively.
• Figure 3: Construction of $G_{\text{adv}}[ij]$.
• Figure 4: The sources and sinks at station E.
• Figure 5: Effect of Physical Knowledge on MAE.