Continuous-time air pollutant forecasting using multi-timescale attention neural ordinary differential equations (MA-NODE)

Air pollution, a major global health and environmental threat, necessitates accurate forecasting to support timely interventions and policy-making. Data-driven approaches, increasingly powered by artificial intelligence (AI), have gained traction in air quality prediction, leveraging their capacity to model complex, nonlinear patterns in environmental data. Deep learning models, such as Long Short-Term Memory (LSTM) networks, excel at capturing temporal dependencies but are hindered by their discrete-time framework, overlooking the continuous dynamics of air pollution driven by physical and chemical processes. This limitation compromises their performance, especially with irregular or sparse observations. Neural Ordinary Differential Equations (Neural ODEs), introduced in 2018, offer a continuous-time modeling paradigm by parameterizing derivatives with neural networks, yet their application to environmental sciences remains underexplored, with many implementations retaining single-scale latent dynamics and lacking calibrated uncertainty estimates. Here, we present a novel Multi-timescale Attention Neural ODE (MA-NODE) framework for multi-step air pollution forecasting, marking one of the first such efforts to our knowledge. Its continuous-time formulation reduces multi-step discretization error and natively accommodates irregular sampling, addressing key limitations of discrete-time deep models. Our model decomposes latent dynamics into fast, medium, and slow timescales, reflecting diverse temporal behaviors, and integrates an attention mechanism to enhance feature synthesis. Evaluated on real-world datasets encompassing PM2.5, O3, NO2, SO2, CO, and PM10, it achieves an R² exceeding 0.9 for three-step-ahead predictions, outperforming traditional and state-of-the-art methods, with 10-15% lower MAE/RMSE and well-calibrated 95% interval coverage (≈ 0.90). This work advances air quality forecasting by harnessing Neural ODEs' continuous modeling capabilities, while operating directly on station observations without gridded meteorology, offering a robust tool for environmental management. By bridging computational innovation with ecological needs, it paves the way for broader Neural ODE applications in environmental science, strengthening public health and sustainability efforts.