$PAS^2$: Physics-Anchored Spectral Reasoning for Air Quality Forecasting

Given the profound impacts on human health and ecosystems, air pollution necessitates robust quality prediction to inform policy-making. Traditional physics-based forecasting relies on idealized closed-system assumptions, whereas data-driven approaches often lack interpretability. Recent hybrid methods, however, neglect data homogeneity, resulting in redundancy, parameter inefficiency, and gradient conflicts. Moreover, high-concentration regions inherently exhibit drastic fluctuations, making it difficult to explicitly distinguish them from the overall pollution field, especially when using spatial information alone. To address these limitations, a Physics-Anchored Spatial-Spectral ($PAS^2$) paradigm is proposed. Specifically, a collaboration scheme is firstly elaborated, within which a physical estimator captures deterministic trends, anchoring the neural branch’s input space and directing it to learn complementary fluctuations. Building on this, we equip the neural branch with a Spatial–Spectral ($S^2$) Reasoner that integrates graph operators to model local spatial diffusion and spectral operators to explicitly capture the drastic fluctuations in high-concentration regions. Experiments on real-world datasets show that $PAS^2$ consistently improves over strong data-driven and physics-guided baselines, especially under volatile sudden-change scenarios. Codes are attached and will be released at GitHub.