# AirDDE: Multifactor Neural Delay Differential Equations for Air Quality Forecasting

arXiv: https://arxiv.org/abs/2603.17529 · HTML: https://mlsanity.com/paper/2603.17529/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 46 references that are in the map.
- First posted on arXiv 18 Mar 2026.

## Builds on (most cited first, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [TFB: Towards Comprehensive and Fair Benchmarking of Time Series Forecasting Methods](https://mlsanity.com/paper/2403.20150/) (2024)
- [Spatial-Temporal Graph ODE Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2106.12931/) (2021)
- [Graph Neural Controlled Differential Equations for Traffic Forecasting](https://mlsanity.com/paper/2112.03558/) (2021)
- [Spatio-Temporal Meta-Graph Learning for Traffic Forecasting](https://mlsanity.com/paper/2211.14701/) (2022)
- [AirFormer: Predicting Nationwide Air Quality in China with Transformers](https://mlsanity.com/paper/2211.15979/) (2022)
- [PM2.5-GNN: A Domain Knowledge Enhanced Graph Neural Network For PM2.5 Forecasting](https://mlsanity.com/paper/2002.12898/) (2020)
- [Joint Air Quality and Weather Prediction Based on Multi-Adversarial Spatiotemporal Networks](https://mlsanity.com/paper/2012.15037/) (2020)
- ["Hey, that's not an ODE": Faster ODE Adjoints via Seminorms](https://mlsanity.com/paper/2009.09457/) (2020)
- [Group-Aware Graph Neural Network for Nationwide City Air Quality Forecasting](https://mlsanity.com/paper/2108.12238/) (2021)
- [Neural Delay Differential Equations](https://mlsanity.com/paper/2102.10801/) (2021)
- [A Foundation Model for the Earth System](https://mlsanity.com/paper/2405.13063/) (2024)
- [Deep Air Learning: Interpolation, Prediction, and Feature Analysis of Fine-grained Air Quality](https://mlsanity.com/paper/1711.00939/) (2017)
- [WeatherGNN: Exploiting Meteo- and Spatial-Dependencies for Local Numerical Weather Prediction Bias-Correction](https://mlsanity.com/paper/2310.05517/) (2023)
- [HighAir: A Hierarchical Graph Neural Network-Based Air Quality Forecasting Method](https://mlsanity.com/paper/2101.04264/) (2021)
- [Spatio-Temporal Field Neural Networks for Air Quality Inference](https://mlsanity.com/paper/2403.02354/) (2024)
- [Signed Graph Neural Ordinary Differential Equation for Modeling Continuous-time Dynamics](https://mlsanity.com/paper/2312.11198/) (2023)
- [DSTCGCN: Learning Dynamic Spatial-Temporal Cross Dependencies for Traffic Forecasting](https://mlsanity.com/paper/2307.00518/) (2023)
- [FuXi-Air: Urban Air Quality Forecasting Based on Emission-Meteorology-Pollutant multimodal Machine Learning](https://mlsanity.com/paper/2506.07616/) (2025)

## Built on by (most cited first, 1 of 1)

- [MUSE: Dependency-Aware Adaptation of a Frozen Vision Backbone for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2609.24441/) (2026)

## Abstract (arXiv)

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.