aiqbench analysis
StationPDE bridges the gap between statistical weather models and physics-informed approaches by learning partial differential equations directly from discrete surface station data without requiring upper-air variables. By decomposing physical evolution into wind transport and learnable diffusion, the model achieves a 9.6% reduction in mean squared error compared to current baselines on standard weather datasets. This advancement demonstrates how integrating explicit physical dynamics with deep learning can significantly improve multivariate forecasting accuracy for discrete observation networks.
StationPDE: Station-Oriented Surface PDE Learning for Multi-Station Multivariate Weather Forecasting
arXiv:2609.22123v1 Announce Type: new Abstract: Multi-station multivariate weather forecasting aims to forecast future weather variables at multiple weather stations from historical surface observations. Existing station forecasting models learn statistical dependencies among discrete stations, but lack explicit physical evolution. Meanwhile, PDE-based weather models provide interpretable physical dynamics, yet require continuous fields and upper-air variables unavailable in surface station data. To bridge this gap, we propose StationPDE, a station-oriented surface PDE learning model. StationPDE constructs a terrain-aware continuous surface field from discrete station observations and decomposes its physical evolution into surface wind transport and upper-air inference. Surface wind transport explicitly evolves observable weather variables, while upper-air inference uses learnable horizontal diffusion to approximate the missing influence of unavailable upper-air variables. A parallel data-driven diffusion branch captures complementary motion patterns, and an adaptive router integrates the two forecasts for station-level multivariate forecasting. Experiments on Weather2K and MeteoNet show that StationPDE consistently outperforms state-of-the-art baselines, reducing MSE by about $9.6\%$ on average compared with the strongest baseline. Code and implementation details are available at https://github.com/hnu-vis/StationPDE.
Abstract:Multi-station multivariate weather forecasting aims to forecast future weather variables at multiple weather stations from historical surface observations. Existing station forecasting models learn statistical dependencies among discrete stations, but lack explicit physical evolution. Meanwhile, PDE-based weather models provide interpretable physical dynamics, yet require continuous fields and upper-air variables unavailable in surface station data. To bridge this gap, we propose StationPDE, a station-oriented surface PDE learning model. StationPDE constructs a terrain-aware continuous surface field from discrete station observations and decomposes its physical evolution into surface wind transport and upper-air inference. Surface wind transport explicitly evolves observable weather variables, while upper-air inference uses learnable horizontal diffusion to approximate the missing influence of unavailable upper-air variables. A parallel data-driven diffusion branch captures complementary motion patterns, and an adaptive router integrates the two forecasts for station-level multivariate forecasting. Experiments on Weather2K and MeteoNet show that StationPDE consistently outperforms state-of-the-art baselines, reducing MSE by about $9.6\%$ on average compared with the strongest baseline. Code and implementation details are available at this https URL.
Machine Learning (cs.LG)
arXiv:2609.22123 [cs.LG]
(or arXiv:2609.22123v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.22123 Focus to learn more arXiv-issued DOI via DataCite
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