STeP-Diff: Spatio-Temporal Physics-Informed Diffusion Models for Mobile Fine-Grained Pollution Forecasting

2025-12-03

AI Summary

This work addresses the challenge of forecasting fine-grained air pollution from incomplete, time-varying, and spatially sparse measurements collected by mobile sensors mounted on non-dedicated platforms (e.g., buses, taxis). To this end, we propose a physics-informed spatiotemporal diffusion model. Methodologically, we innovatively embed constraints from the advection–diffusion partial differential equation (PDE) into the denoising process of a diffusion model, ensuring that generated trajectories asymptotically conform to underlying physical laws. We further incorporate DeepONet to capture spatial heterogeneity and jointly optimize observational data and prior physical knowledge via physics-informed neural network (PINN)-based PDE regularization. Evaluated on real-world measurements from 59 mobile nodes across two cities, our method outperforms the best baseline by 89.12% in MAE, 82.30% in RMSE, and 25.00% in MAPE—demonstrating substantial improvements in prediction accuracy and generalization under sparse, non-uniform sampling conditions.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Computer Vision: Diffusion Models for Vision
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Fine-grained air pollution forecasting is crucial for urban management and the development of healthy buildings. Deploying portable sensors on mobile platforms such as cars and buses offers a low-cost, easy-to-maintain, and wide-coverage data collection solution. However, due to the random and uncontrollable movement patterns of these non-dedicated mobile platforms, the resulting sensor data are often incomplete and temporally inconsistent. By exploring potential training patterns in the reverse process of diffusion models, we propose Spatio-Temporal Physics-Informed Diffusion Models (STeP-Diff). STeP-Diff leverages DeepONet to model the spatial sequence of measurements along with a PDE-informed diffusion model to forecast the spatio-temporal field from incomplete and time-varying data. Through a PDE-constrained regularization framework, the denoising process asymptotically converges to the convection-diffusion dynamics, ensuring that predictions are both grounded in real-world measurements and aligned with the fundamental physics governing pollution dispersion. To assess the performance of the system, we deployed 59 self-designed portable sensing devices in two cities, operating for 14 days to collect air pollution data. Compared to the second-best performing algorithm, our model achieved improvements of up to 89.12% in MAE, 82.30% in RMSE, and 25.00% in MAPE, with extensive evaluations demonstrating that STeP-Diff effectively captures the spatio-temporal dependencies in air pollution fields.

Problem

• Forecasting fine-grained air pollution from incomplete mobile sensor data
• Modeling spatio-temporal dependencies with physics-informed diffusion models
• Improving prediction accuracy using PDE-constrained regularization framework

Innovation

• Uses diffusion models with DeepONet for spatial sequence modeling
• Incorporates PDE-informed regularization for physics-aligned pollution forecasting
• Leverages portable sensors on mobile platforms for data collection