Physics-Guided Inductive Spatiotemporal Kriging for PM2.5 with Satellite Gradient Constraints

TL;DR

This paper introduces SPIN, a physics-guided inductive graph neural network for high-resolution $PM_{2.5}$ mapping under sparse ground networks. By embedding advection and diffusion kernels and employing a novel Masked AOD Spatial Gradient Loss, SPIN reframes satellite data as a gradient constraint rather than a direct input, enabling robust inductive kriging for Station and Grid Inference. The approach achieves state-of-the-art performance on the Beijing-Tianjin-Hebei region with a MAE of $9.52\ \mu\text{g}/\text{m}^3$, and demonstrates strong robustness to 50% station dropout while generating physically plausible fields in unmonitored areas. SPIN's all-weather, low-cost inference capability has significant implications for urban environmental management, offering a virtual sensing network and real-time decision support beyond traditional CTMs.

Abstract

High-resolution mapping of fine particulate matter (PM2.5) is a cornerstone of sustainable urbanism but remains critically hindered by the spatial sparsity of ground monitoring networks. While traditional data-driven methods attempt to bridge this gap using satellite Aerosol Optical Depth (AOD), they often suffer from severe, non-random data missingness (e.g., due to cloud cover or nighttime) and inversion biases. To overcome these limitations, this study proposes the Spatiotemporal Physics-Guided Inference Network (SPIN), a novel framework designed for inductive spatiotemporal kriging. Unlike conventional approaches, SPIN synergistically integrates domain knowledge into deep learning by explicitly modeling physical advection and diffusion processes via parallel graph kernels. Crucially, we introduce a paradigm-shifting training strategy: rather than using error-prone AOD as a direct input, we repurpose it as a spatial gradient constraint within the loss function. This allows the model to learn structural pollution patterns from satellite data while remaining robust to data voids. Validated in the highly polluted Beijing-Tianjin-Hebei and Surrounding Areas (BTHSA), SPIN achieves a new state-of-the-art with a Mean Absolute Error (MAE) of 9.52 ug/m^3, effectively generating continuous, physically plausible pollution fields even in unmonitored areas. This work provides a robust, low-cost, and all-weather solution for fine-grained environmental management.

Figures (7)

• Figure 1: Study area and task setup. (a) The "2+26" cities in the BTHSA region. (b) A spatial adjacency graph constructed by connecting monitoring stations within a 200km geodesic thresholdqi2019hybridwang2021modeling. (c) Sparse distribution of the 152 ground monitoring stations. (d) The $0.25^{\circ}$ grid used for dense map inference, where most cells lack ground truth.
• Figure 2: Architecture of SPIN. The model first encodes local temporal dynamics via TCN. It then propagates spatial information via a Physics-Guided Graph Network, driven by two explicit kernels: a Diffusion Kernel (isotropic spreading) and an Advection Kernel (wind-driven transport). Finally, the training is constrained by a novel Masked AOD Gradient Loss to ensure structural consistency with satellite observations.
• Figure 3: Physical Kernels and AOD Constraint. (a) The Advection Kernel weights edges based on wind velocity projections, modeling directional transport. (b) The AOD Gradient Loss aligns the spatial difference of predictions with AOD, active only on valid pixels (shaded area), ensuring robustness to missing data.
• Figure 4: Inference performance across core cities in the BTHSA region. From top to bottom: Beijing (Station 1002A), Tianjin (Station 1018A), and Shijiazhuang (Station 1034A). Despite being completely unobserved during training, the model accurately tracks the ground truth (blue) with high correlation ($R^2 > 0.85$) across these geographically distinct urban centers, successfully capturing the complex winter pollution cycles.
• Figure 5: Performance bounds analysis. Top: The best-performing case (Station 2409A) shows near-perfect reconstruction due to dense neighbor support. Bottom: The worst-case scenario (Station 2396A) still maintains correct trend directionality, demonstrating stability under challenging topology.