# Air Quality Prediction with Physics-Guided Dual Neural ODEs in Open Systems

arXiv: https://arxiv.org/abs/2410.19892 · HTML: https://mlsanity.com/paper/2410.19892/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 53 references that are in the map.
- First posted on arXiv 25 Oct 2024.

## Builds on (most cited first, 27 of 27)

- [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)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [TFB: Towards Comprehensive and Fair Benchmarking of Time Series Forecasting Methods](https://mlsanity.com/paper/2403.20150/) (2024)
- [Discrete Graph Structure Learning for Forecasting Multiple Time Series](https://mlsanity.com/paper/2101.06861/) (2021)
- [Pathformer: Multi-scale Transformers with Adaptive Pathways for Time Series Forecasting](https://mlsanity.com/paper/2402.05956/) (2024)
- [CATCH: Channel-Aware multivariate Time Series Anomaly Detection via Frequency Patching](https://mlsanity.com/paper/2410.12261/) (2024)
- [Learning Long-Term Dependencies in Irregularly-Sampled Time Series](https://mlsanity.com/paper/2006.04418/) (2020)
- [ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEs](https://mlsanity.com/paper/2404.10024/) (2024)
- [AirFormer: Predicting Nationwide Air Quality in China with Transformers](https://mlsanity.com/paper/2211.15979/) (2022)
- [An Evaluation of Change Point Detection Algorithms](https://mlsanity.com/paper/2003.06222/) (2020)
- [PM2.5-GNN: A Domain Knowledge Enhanced Graph Neural Network For PM2.5 Forecasting](https://mlsanity.com/paper/2002.12898/) (2020)
- [GREAD: Graph Neural Reaction-Diffusion Networks](https://mlsanity.com/paper/2211.14208/) (2022)
- [Learning continuous-time PDEs from sparse data with graph neural networks](https://mlsanity.com/paper/2006.08956/) (2020)
- [LightTS: Lightweight Time Series Classification with Adaptive Ensemble Distillation -- Extended Version](https://mlsanity.com/paper/2302.12721/) (2023)
- [STDEN: Towards Physics-Guided Neural Networks for Traffic Flow Prediction](https://mlsanity.com/paper/2209.00225/) (2022)
- [Towards a General Time Series Anomaly Detector with Adaptive Bottlenecks and Dual Adversarial Decoders](https://mlsanity.com/paper/2405.15273/) (2024)
- [AirPhyNet: Harnessing Physics-Guided Neural Networks for Air Quality Prediction](https://mlsanity.com/paper/2402.03784/) (2024)
- [Generalizing Weather Forecast to Fine-grained Temporal Scales via Physics-AI Hybrid Modeling](https://mlsanity.com/paper/2405.13796/) (2024)
- [Climate Modeling with Neural Diffusion Equations](https://mlsanity.com/paper/2111.06011/) (2021)
- [Knowledge-guided Machine Learning: Current Trends and Future Prospects](https://mlsanity.com/paper/2403.15989/) (2024)
- [Machine Learning for Urban Air Quality Analytics: A Survey](https://mlsanity.com/paper/2310.09620/) (2023)
- [Novel Physics-Based Machine-Learning Models for Indoor Air Quality Approximations](https://mlsanity.com/paper/2308.01438/) (2023)
- [QCore: Data-Efficient, On-Device Continual Calibration for Quantized Models -- Extended Version](https://mlsanity.com/paper/2404.13990/) (2024)
- [Physics-Informed Deep Learning to Reduce the Bias in Joint Prediction of Nitrogen Oxides](https://mlsanity.com/paper/2308.07441/) (2023)

## Built on by (most cited first, 26 of 26)

- [Aurora: Towards Universal Generative Multimodal Time Series Forecasting](https://mlsanity.com/paper/2509.22295/) (2025)
- [GCGNet: Graph-Consistent Generative Network for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2603.08032/) (2026)
- [Learning Generalizable Skills from Offline Multi-Task Data for Multi-Agent Cooperation](https://mlsanity.com/paper/2503.21200/) (2025)
- [ARROW: An Adaptive Rollout and Routing Method for Global Weather Forecasting](https://mlsanity.com/paper/2510.09734/) (2025)
- [USTBench: Benchmarking and Dissecting Spatiotemporal Reasoning of LLMs as Urban Agents](https://mlsanity.com/paper/2505.17572/) (2025)
- [Unlocking the Value of Text: Event-Driven Reasoning and Multi-Level Alignment for Time Series Forecasting](https://mlsanity.com/paper/2603.15452/) (2026)
- [RCRank: Multimodal Ranking of Root Causes of Slow Queries in Cloud Database Systems](https://mlsanity.com/paper/2503.04252/) (2025)
- [Towards Multimodal Time Series Anomaly Detection with Semantic Alignment and Condensed Interaction](https://mlsanity.com/paper/2603.21612/) (2026)
- [Exploring Graph Mamba: A Comprehensive Survey on State-Space Models for Graph Learning](https://mlsanity.com/paper/2412.18322/) (2024)
- [Data Driven Decision Making with Time Series and Spatio-temporal Data](https://mlsanity.com/paper/2503.08473/) (2025)
- [A Survey of Physics-Informed AI for Complex Urban Systems](https://mlsanity.com/paper/2506.13777/) (2025)
- [S2Transformer: Scalable Structured Transformers for Global Station Weather Forecasting](https://mlsanity.com/paper/2509.19648/) (2025)
- [Learning to Factorize and Adapt: A Versatile Approach Toward Universal Spatio-Temporal Foundation Models](https://mlsanity.com/paper/2601.12083/) (2026)
- [TiWeaver: Unified Temporal Dynamics Modeling via Contextual Patching](https://mlsanity.com/paper/2606.03121/) (2026)
- [A Causality-Aware Spatiotemporal Model for Multi-Region and Multi-Pollutant Air Quality Forecasting](https://mlsanity.com/paper/2509.21260/) (2025)
- [Breaking the Regional Barrier: Inductive Semantic Topology Learning for Worldwide Air Quality Forecasting](https://mlsanity.com/paper/2601.21899/) (2026)
- [Nested Spatio-Temporal Time Series Forecasting](https://mlsanity.com/paper/2605.16447/) (2026)
- [Air Quality Prediction with A Meteorology-Guided Modality-Decoupled Spatio-Temporal Network](https://mlsanity.com/paper/2504.10014/) (2025)
- [Double-Diffusion: Balancing Speed, Accuracy, and Uncertainty in Probabilistic Forecasting for Urban Sensor Networks](https://mlsanity.com/paper/2506.23053/) (2025)
- [Epi2-Net: Advancing Epidemic Dynamics Forecasting with Physics-Inspired Neural Networks](https://mlsanity.com/paper/2508.02049/) (2025)
- [SSTODE: Ocean-Atmosphere Physics-Informed Neural ODEs for Sea Surface Temperature Prediction](https://mlsanity.com/paper/2511.05629/) (2025)
- [NeuroDDAF: Neural Dynamic Diffusion-Advection Fields with Evidential Fusion for Air Quality Forecasting](https://mlsanity.com/paper/2604.01175/) (2026)
- [TrafficClaw: A Generalizable LLM Agent in the Unified Physical Environment for Urban Traffic Control](https://mlsanity.com/paper/2604.17456/) (2026)
- [Physics-Informed Super-Resolution of Atmospheric Data](https://mlsanity.com/paper/2607.18877/) (2026)
- [AirFlow: Context Preserving and Multi-Rate State Modeling for Air Quality Forecasting](https://mlsanity.com/paper/2608.09775/) (2026)
- [AeroChem: Closed-loop Physics-Informed State Space Modeling for Long-term Chemically-Reactive Air Quality Forecasting--Extended Version](https://mlsanity.com/paper/2610.16630/) (2026)

## Abstract (arXiv)

Air pollution significantly threatens human health and ecosystems, necessitating effective air quality prediction to inform public policy. Traditional approaches are generally categorized into physics-based and data-driven models. Physics-based models usually struggle with high computational demands and closed-system assumptions, while data-driven models may overlook essential physical dynamics, confusing the capturing of spatiotemporal correlations. Although some physics-guided approaches combine the strengths of both models, they often face a mismatch between explicit physical equations and implicit learned representations. To address these challenges, we propose Air-DualODE, a novel physics-guided approach that integrates dual branches of Neural ODEs for air quality prediction. The first branch applies open-system physical equations to capture spatiotemporal dependencies for learning physics dynamics, while the second branch identifies the dependencies not addressed by the first in a fully data-driven way. These dual representations are temporally aligned and fused to enhance prediction accuracy. Our experimental results demonstrate that Air-DualODE achieves state-of-the-art performance in predicting pollutant concentrations across various spatial scales, thereby offering a promising solution for real-world air quality challenges.