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Interpretable Air Pollution Forecasting by Physics-Guided Spatiotemporal Decoupling

Zhiguo Zhang, Xiaoliang Ma, Daniel Schlesinger

TL;DR

This work tackles the challenge of accurate and interpretable urban air quality forecasting by introducing a physics-guided spatiotemporal framework that decouples transport and local dynamics into two additive modules. A wind-conditioned, dynamic advection kernel models cross-station transport, while a station-wise interpretable attention encoder captures local temporal dependencies and attributions. The approach provides spatiotemporal interpretability through dynamic upwind weights and attention-based local attributions, and demonstrates superior predictive performance on a Stockholm PM$_{10}$ dataset relative to state-of-the-art baselines. Practically, the method offers reliable forecasts with transparent explanations suitable for operational air-quality management, and the experimental results include a case study that corroborates meteorology-consistent attributions. Overall, the combination of a learnable physics prior with an interpretable neural architecture delivers both accuracy and diagnostic insight for city-scale air pollution forecasting.

Abstract

Accurate and interpretable air pollution forecasting is crucial for public health, but most models face a trade-off between performance and interpretability. This study proposes a physics-guided, interpretable-by-design spatiotemporal learning framework. The model decomposes the spatiotemporal behavior of air pollutant concentrations into two transparent, additive modules. The first is a physics-guided transport kernel with directed weights conditioned on wind and geography (advection). The second is an explainable attention mechanism that learns local responses and attributes future concentrations to specific historical lags and exogenous drivers. Evaluated on a comprehensive dataset from the Stockholm region, our model consistently outperforms state-of-the-art baselines across multiple forecasting horizons. Our model's integration of high predictive performance and spatiotemporal interpretability provides a more reliable foundation for operational air-quality management in real-world applications.

Interpretable Air Pollution Forecasting by Physics-Guided Spatiotemporal Decoupling

TL;DR

This work tackles the challenge of accurate and interpretable urban air quality forecasting by introducing a physics-guided spatiotemporal framework that decouples transport and local dynamics into two additive modules. A wind-conditioned, dynamic advection kernel models cross-station transport, while a station-wise interpretable attention encoder captures local temporal dependencies and attributions. The approach provides spatiotemporal interpretability through dynamic upwind weights and attention-based local attributions, and demonstrates superior predictive performance on a Stockholm PM dataset relative to state-of-the-art baselines. Practically, the method offers reliable forecasts with transparent explanations suitable for operational air-quality management, and the experimental results include a case study that corroborates meteorology-consistent attributions. Overall, the combination of a learnable physics prior with an interpretable neural architecture delivers both accuracy and diagnostic insight for city-scale air pollution forecasting.

Abstract

Accurate and interpretable air pollution forecasting is crucial for public health, but most models face a trade-off between performance and interpretability. This study proposes a physics-guided, interpretable-by-design spatiotemporal learning framework. The model decomposes the spatiotemporal behavior of air pollutant concentrations into two transparent, additive modules. The first is a physics-guided transport kernel with directed weights conditioned on wind and geography (advection). The second is an explainable attention mechanism that learns local responses and attributes future concentrations to specific historical lags and exogenous drivers. Evaluated on a comprehensive dataset from the Stockholm region, our model consistently outperforms state-of-the-art baselines across multiple forecasting horizons. Our model's integration of high predictive performance and spatiotemporal interpretability provides a more reliable foundation for operational air-quality management in real-world applications.

Paper Structure

This paper contains 23 sections, 20 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Spatiotemporal Forecasting
  4. Physics-Guided Models
  5. Preliminaries
  6. Problem Formulation
  7. Governing Equations and Model Formulation
  8. Methodology
  9. Embedding of Time-Feature Tokens
  10. Station-wise Local Dynamics Encoder
  11. Physics-Guided Cross-Station Transport
  12. Local Geometry and Upwind Alignment
  13. Physics-Guided Adjacency Score
  14. Upwind Spatial Aggregation
  15. Fusion and Decoding
  16. ...and 8 more sections

Figures (4)

  • Figure 1: An overview of the proposed model.
  • Figure 2: The embedding and attention mechanism for modeling local dynamics.
  • Figure 3: The physics-guided module for cross-station transport.
  • Figure 4: (a) Dynamic spatial attribution for the S:t Eriksgatan forecast. Each bar represents a 12-hour forecast patch, with the percentage contribution from each upwind station, as determined by the learned spatial weights $\mathbf{W}^{\mathrm{sp}}_m$; (b) Local temporal-feature attribution for a 72-hour forecast at S:t Eriksgatan. The color intensity indicating the influence of each input feature patch on each future prediction patch; (c) The distribution of wind direction and speed, serving as meteorological ground truth to validate the learned spatial attributions in (a).