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

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.