AirPCM: Deep Spatiotemporal Air Quality Forecasting

• AirPCM is a causality-aware deep spatiotemporal model that integrates spatial dependency, pollutant dynamics, and meteorology–pollutant causality for accurate air quality forecasting.
• It employs modules such as multi-station spatial correlation, patch embedding, and temporal causal attention to capture complex cross-station and cross-pollutant interactions.
• AirPCM demonstrates significant performance gains over baselines on multiple benchmarks while providing interpretable insights into meteorological influences on pollutant levels.

AirPCM is a causality-aware deep spatiotemporal model designed for multi-region and multi-pollutant air quality forecasting. It leverages a unified architecture to jointly capture cross-station spatial dependencies, complex pollutant and meteorological dynamics, and explicit meteorology–pollutant causality. AirPCM addresses challenges inherent to distributed air-quality forecasting, including spatial heterogeneity, intricate cross-pollutant interactions, and the need for interpretable, fine-grained predictions across diverse temporal and geographic scales (Lu et al., 25 Sep 2025).

1. Mathematical Formulation and Problem Setup

The junction of data assimilation and spatiotemporal modeling in AirPCM begins with formalizing the multi-region, multi-pollutant forecasting problem. Let $N$ denote the number of monitoring stations, $K$ the number of pollutants, and $C$ the number of meteorological variables. At each time $t$:

• $x_t \in \mathbb{R}^{N \times K}$: matrix of pollutant concentrations.
• $m_t \in \mathbb{R}^{N \times C}$: matrix of meteorological features (e.g., temperature, humidity).

Given historical windows $X_{t-\tau:t} \in \mathbb{R}^{N\times K\times \tau}$ and $M_{t-\tau:t} \in \mathbb{R}^{N\times C\times \tau}$ of length $\tau$, the goal is to predict the next $\kappa$-step pollutant concentration maps: $K$0.

The learning objective is to minimize the mean-squared error (MSE):

$K$1

with $K$2, where $K$3 is the AirPCM model.

2. Architecture Components

AirPCM’s architecture consists of four sequential modules, each addressing a distinct axis of spatiotemporal prediction:

1. Multi-Station Spatial Correlation Modeling (MSCM): Constructs a geographic graph $K$4 using spatial coordinates of stations, modeling both local and non-local spatial dependencies with a convolutional layer, a Graph Attention Network (GAT), and a multi-head self-attention (MSA). This yields spatially-refined features $K$5.
2. Patching & Embedding (P E): Segments the temporal pollutant sequence for each channel into $K$6 overlapping patches, then embeds each by combining content, position, and time encodings. The result is a set of patch embeddings $K$7 per pollutant.
3. Meteorology–Pollutant Temporal Causality (MPTC): Applies the MSCM stack to meteorological data, extracts a causal window of the most recent $K$8 steps, and embeds this as $K$9. A multi-head causal attention mechanism with a lower-triangular mask then computes the temporally-constrained influence of meteorological history on each pollutant patch, producing $C$0.
4. Decoding (DECO): Fuses $C$1 and $C$2, and processes the fused representation via $C$3 temporal self-attention blocks (with feed-forward sublayers) to model residual time-series dynamics, followed by per-pollutant adapters and output projections to generate $C$4-step forecasts.

3. Training Procedure and Inference

AirPCM is trained end-to-end with the Adam optimizer. Typical hyperparameters include a learning rate of $C$5, batch size of 64, 8 attention heads, $C$6, $C$7, and $C$8. The overall training and inference workflow is as follows:

1. Generate spatial features using MSCM for pollutant and meteorological histories.
2. Form temporal patches and compute embeddings.
3. Compute meteorology–pollutant causal attention with masking.
4. Fuse embeddings and pass through DECO’s stacked attention blocks.
5. Forecast for all pollutants over the prediction horizon.
6. Compute loss (MSE) and update parameters.

During inference, the forward computation mirrors steps 1–5 above, applied to the most recent observation windows.

4. Data Resources and Experimental Protocols

AirPCM is evaluated across four real-world benchmarks:

• Beijing (city-scale): 35 stations, hourly records (2017–05–2018–05), 6 pollutants + 5 meteorological variables.
• KnowAir (national-scale, China): 184 cities, 3-hour intervals (2015–2018), PM$C$9 + 17 meteorological features.
• AirPCM-d (daily): 156 stations, China-wide, daily records (2015–2025), 6 pollutants + 5 meteorological variables + AQI.
• AirPCM-h (hourly, global): 453 stations (363 China, 55 Europe, 35 US), hourly Jan 2024–Apr 2025, 6 pollutants + 5 meteorological variables.

Dataset processing involves a 2:1:1 train/validation/test split, linear interpolation of missing values, and min–max normalization. Evaluation metrics are MAE, RMSE, and SMAPE, with separate reporting for all-step and high-magnitude “sudden-change” episodes (where PM$t$0 varies by more than 20 μg/m³).

5. Quantitative Performance and Comparative Analysis

AirPCM consistently yields superior performance versus state-of-the-art baselines across datasets and forecast horizons. For 3-day PM$t$1 forecasting (Beijing sudden changes), AirPCM reduces MAE and RMSE compared to Air-DualODE and AirPhyNet. In “sudden-change” conditions, AirPCM achieved, for KnowAir:

Method	MAE	RMSE	SMAPE
Air-DualODE	66.40	90.31	0.73
AirPCM	61.85	84.34	0.64
Gain (%)	+6.9%	+6.6%	+12.3%

On the global AirPCM-h dataset, AirPCM reduces 72-h RMSE by 5–10% against top baselines and maintains superior short-/mid-term accuracy. Transfer experiments (Beijing$t$2US, KnowAir$t$3China) confirm robust spatiotemporal generalization, as AirPCM shows the lowest MAE/RMSE across all prediction horizons (Lu et al., 25 Sep 2025).

6. Ablation, Interpretability, and Causal Insights

Ablation analysis demonstrates the necessity of each architectural block:

• Removing MSCM (graph-attention + spatial MSA) degrades RMSE by approximately 8%.
• Replacing the temporal patch+attention design with a single LSTM increases MAE by about 6%.
• Omitting the MPTC causal attention (feeding only pollutant history) leads to a ~10% higher SMAPE.

Analysis of causal attention weights demonstrates physically plausible attributions; for example, a lagged positive effect of temperature (24h) on O$t$4, and a negative effect of humidity (12–36h lags) on PM$t$5. This suggests AirPCM’s attention mechanism encodes interpretable, physically meaningful meteorology-pollutant relationships.

7. Representative Applications and Case Studies

AirPCM supports both long-term trend forecasting and the detection of sudden events:

• Long-Term Forecasting (AirPCM-d): Forecasts AQI categories and pollutant trends through April 2027, revealing a persistent north-south gradient in “unhealthy” days across China, with regional meteorological causation (e.g., more frequent inversions in the North China Plain). In Beijing, an overall decline in winter pollution episodes is noted, whereas O$t$6 levels exhibit an uptick post-2025, corresponding to secondary formation dynamics under NO$t$7-limited regimes.
• Sudden Pollution Episodes: AirPCM more accurately captures the onset and decay of sharp PM$t$8 fluctuations than competing baselines, evidenced by lower lag and error, and a 12.3% reduction in SMAPE and 6.6% reduction in RMSE on KnowAir “sudden-change” tests.

A plausible implication is that AirPCM’s unified modeling of spatial, temporal, and meteorological-causal dependencies enhances resilience to both gradual trends and abrupt, disturbance-driven dynamics in air pollution systems.

---

AirPCM consolidates graph- and attention-based methodologies for interpretable, accurate, and scalable multi-region, multi-pollutant air quality forecasting, systematically outperforming state-of-the-art baselines and supporting evidence-driven environmental forecasting and governance (Lu et al., 25 Sep 2025).