AirDDE: Multifactor Neural Delay Differential Equations for Air Quality Forecasting

Accurate air quality forecasting is essential for public health and environmental sustainability, but remains challenging due to the complex pollutant dynamics. Existing deep learning methods often model pollutant dynamics as an instantaneous process, overlooking the intrinsic delays in pollutant propagation. Thus, we propose AirDDE, the first neural delay differential equation framework in this task that integrates delay modeling into a continuous-time pollutant evolution under physical guidance. Specifically, two novel components are introduced: (1) a memory-augmented attention module that retrieves globally and locally historical features, which can adaptively capture delay effects modulated by multifactor data; and (2) a physics-guided delay evolving function, grounded in the diffusion-advection equation, that models diffusion, delayed advection, and source/sink terms, which can capture delay-aware pollutant accumulation patterns with physical plausibility. Extensive experiments on three real-world datasets demonstrate that AirDDE achieves the state-of-the-art forecasting performance with an average MAE reduction of 8.79\% over the best baselines. The code is available at https://github.com/w2obin/airdde-aaai.

MillGNN: Learning Multi-Scale Lead-Lag Dependencies for Multi-Variate Time Series Forecasting

Multi-variate time series (MTS) forecasting is crucial for various applications. Existing methods have shown promising results owing to their strong ability to capture intra- and inter-variate dependencies. However, these methods often overlook lead-lag dependencies at multiple grouping scales, failing to capture hierarchical lead-lag effects in complex systems. To this end, we propose MillGNN, a novel \underline{g}raph \underline{n}eural \underline{n}etwork-based method that learns \underline{m}ult\underline{i}ple grouping scale \underline{l}ead-\underline{l}ag dependencies for MTS forecasting, which can comprehensively capture lead-lag effects considering variate-wise and group-wise dynamics and decays. Specifically, MillGNN introduces two key innovations: (1) a scale-specific lead-lag graph learning module that integrates cross-correlation coefficients and dynamic decaying features derived from real-time inputs and time lags to learn lead-lag dependencies for each scale, which can model evolving lead-lag dependencies with statistical interpretability and data-driven flexibility; (2) a hierarchical lead-lag message passing module that passes lead-lag messages at multiple grouping scales in a structured way to simultaneously propagate intra- and inter-scale lead-lag effects, which can capture multi-scale lead-lag effects with a balance of comprehensiveness and efficiency. Experimental results on 11 datasets demonstrate the superiority of MillGNN for long-term and short-term MTS forecasting, compared with 16 state-of-the-art methods.