How Domain Knowledge Boosts GNN Accuracy for PM2.5 Forecasting

Problem Context

PM2.5 concentration forecasting requires modeling complex multi‑factor coupling (emission sources, meteorological conditions, geographic barriers) and long‑range spatio‑temporal dependencies. Traditional numerical models (e.g., CMAQ) rely on outdated emission inventories and are computationally intensive. Conventional deep‑learning approaches (CNN on fixed grids, static undirected GCN) cannot capture irregular monitoring station layouts or dynamic wind‑driven transmission.

PM2.5‑GNN Architecture

Data Features

Each city node contains a historical PM2.5 value and meteorological variables: planetary boundary layer height (PBL), wind speed, wind direction, temperature, humidity, precipitation, and pressure.

Graph Construction

Nodes represent cities. Directed edges encode potential pollutant transmission. Edge attributes consist of:

Wind speed magnitude |v|

Transmission direction defined by the angle θ between wind direction and the line connecting two cities

Euclidean distance d between the cities

The advection coefficient is computed as S = ReLU(|v| * cos(θ) / d), guaranteeing a non‑negative transmission strength.

Graph Neural Network Module

For each directed edge (j→i), an MLP transforms the concatenation of node j’s features and the edge attributes into an edge representation. Node i aggregates messages from all incoming neighbors using a second MLP, enabling learning of non‑linear spatial interactions while preserving wind‑driven transmission information.

Temporal GRU Module

The hidden state of each node is updated by a GRU. The GRU input is the concatenation of the node’s current feature vector (including current meteorology and historical PM2.5) and the spatial representation produced by the GNN. Update and reset gates balance historical information with new inputs, mitigating gradient‑vanishing for long‑term dependencies.

Output Layer

The final hidden state is passed through an MLP to generate the predicted PM2.5 concentration for the next time step, leveraging the MLP’s strong non‑linear fitting capability.

Experimental Setup

Data Splits

Training set: 2015‑2016 (historical PM2.5 and meteorological records)

Validation set: 2017 (hyper‑parameter tuning)

Test set: 2018 (final performance evaluation)

Baseline Models

MLP – uses only node features, ignores spatial and temporal dependencies.

LSTM / GRU – captures temporal dynamics but lacks spatial structure.

GC‑LSTM – combines static undirected graph convolution with LSTM, cannot handle dynamic directed edges.

Results

PM2.5‑GNN achieves the lowest RMSE and MAE across all three data splits, demonstrating superior spatio‑temporal modeling compared with the baselines.

Ablation Study

Removing the PBL feature or the edge attributes leads to a marked degradation in performance, confirming the importance of vertical diffusion modeling and dynamic edge information for accurate long‑range pollutant transmission.

Case Study: Xi’an

The model accurately predicts local concentration trends under stagnant conditions and captures remote pollution influx from surrounding industrial cities, illustrating its capability to model both short‑range and long‑range dependencies.

Conclusion and Future Directions

Integrating domain knowledge (wind‑driven edge features, PBL) with graph neural networks and GRU yields higher accuracy and computational efficiency than traditional numerical simulators. Future work includes enhancing interpretability, incorporating multimodal data such as satellite AOD, and extending the framework to multi‑regional and cross‑border pollution forecasting.

Reference

Wang, S. et al. "PM2.5‑GNN: A Domain Knowledge Enhanced Graph Neural Network For PM2.5 Forecasting." ACM SIGSPATIAL 163–166 (2020). DOI: 10.1145/3397536.3422208.

Code repository: https://github.com/shuowang-ai/PM2.5-GNN