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Air Quality Prediction with Physics-Guided Dual Neural ODEs in Open Systems
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Proposes Air-DualODE, a physics-guided dual Neural ODE model for air pollutant forecasting that combines an open-system boundary-aware diffusion-advection equation branch with a data-driven latent Neural ODE branch, aligned by decaying temporal contrastive learning and fused via GNN.
Problem
Air quality (PM2.5) forecasting at city and national scales, where closed-system physics assumptions are unrealistic and purely data-driven models ignore physical transport dynamics, and explicit physical equations mismatch implicit latent representations.
Approach
A discrete boundary-aware diffusion-advection equation adds a learned open-system correction term (source/sink coefficient beta) and gates diffusion vs. advection; it runs in parallel with a data-driven Neural ODE branch, and the two latent representations are temporally aligned with a decaying contrastive loss and fused with a GNN.
Key results
- On Beijing 3-day prediction, Air-DualODE achieves MAE 40.32 vs. 42.72 for the next-best AirPhyNet and 42.74 for AirFormer.
- On KnowAir 3-day prediction, Air-DualODE achieves MAE 18.64 and RMSE 29.37, versus 19.17 MAE for the best baselines (AirFormer, MTSF-DG).
- Removing the data-driven branch degrades Beijing MAE from 40.32 to 44.33, showing the complementarity of physics and data-driven dynamics.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add Physics Dynamics to Data-Driven Dynamics (ablation) | Air-DualODE · Beijing | MAE: 42.75 -> 40.32 | Helped |
| add Physics Dynamics to Data-Driven Dynamics (ablation) | Air-DualODE · KnowAir | MAE: 19.69 -> 18.64 | Helped |
| add Data-Driven Dynamics to Physics Dynamics (ablation) | Air-DualODE · Beijing | MAE: 44.33 -> 40.32 | Helped |
| add Data-Driven Dynamics to Physics Dynamics (ablation) | Air-DualODE · KnowAir | MAE: 21.21 -> 18.64 | Helped |
| fuse dynamics in latent space rather than after decoding (ablation) | Air-DualODE · Beijing | MAE: 41.32 -> 40.32 | Helped |
| fuse dynamics in latent space rather than after decoding (ablation) | Air-DualODE · KnowAir | MAE: 19.06 -> 18.64 | Helped |
| align representations with Decay-TCL before fusion (ablation) | Air-DualODE · Beijing | MAE: 42.34 -> 40.32 | Helped |
| align representations with Decay-TCL before fusion (ablation) | Air-DualODE · KnowAir | MAE: 19.10 -> 18.64 | Helped |
| use Spatial-MSA instead of standard self-attention (ablation) | Air-DualODE · Beijing | MAE: 40.52 -> 40.32 | Helped |
| use Spatial-MSA instead of standard self-attention (ablation) | Air-DualODE · KnowAir | MAE: 18.97 -> 18.64 | Helped |
| use GNN Fusion instead of MLP-based or pooling fusion (ablation) | Air-DualODE · Beijing | MAE: 41.49; 41.45; 43.23; 43.12 -> 40.32 | Helped |
| use GNN Fusion instead of MLP-based or pooling fusion (ablation) | Air-DualODE · KnowAir | MAE: 21.50; 21.42; 20.03; 19.97 -> 18.64 | Helped |
Surprising findings
- Sudden-change prediction remains hard: peak concentrations are often poorly predicted despite trend capture.
- Removing layer normalization causes gradient explosion and NaN with the adaptive dopri5 solver.
Limitations
- Sudden-change peaks are not well predicted.
- Adaptive dopri5 solver requires layer normalization for numerical stability.
- Evaluated only on two datasets (Beijing and KnowAir) focused on PM2.5.
Experimental setup
Datasets: Beijing air quality dataset KnowAir dataset
Benchmarks: Beijing KnowAir
Metrics: MAE RMSE SMAPE
Baselines: HA VAR LatentODE ODE-RNN ODE-LSTM STGCN DCRNN ASTGCN GTS MTSF-DG PM25GNN AirFormer
Builds on: Neural ODE Latent-ODE AirPhyNet method of lines dopri5 solver
Closest papers by meaning
- AirPhyNet: Harnessing Physics-Guided Neural Networks for Air Quality Prediction (ICLR 2024 · similarity 0.93)
- Eulerian Neural Network Informed by Chemical Transport for Air Quality Forecasting (NeurIPS 2025 · similarity 0.89)
- SNN-PDE: Learning Dynamic PDEs from Data with Simplicial Neural Networks (AAAI 2024 · similarity 0.84)
- AirRadar: Inferring Nationwide Air Quality in China with Deep Neural Networks (AAAI 2025 · similarity 0.83)
- Physics-Guided Foundation Model for Scientific Discovery: An Application to Aquatic Science (AAAI 2025 · similarity 0.82)
- P$^2$C$^2$Net: PDE-Preserved Coarse Correction Network for efficient prediction of spatiotemporal dynamics (NeurIPS 2024 · similarity 0.82)
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