# StationPDE: Station-Oriented Surface PDE Learning for Multi-Station Multivariate Weather Forecasting

arXiv: https://arxiv.org/abs/2609.22123 · HTML: https://mlsanity.com/paper/2609.22123/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 20 references that are in the map.
- First posted on arXiv 20 Aug 2026.

## Builds on (most cited first, 11 of 11)

- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting](https://mlsanity.com/paper/2405.14616/) (2024)
- [Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting](https://mlsanity.com/paper/2103.07719/) (2021)
- [TimeXer: Empowering Transformers for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2402.19072/) (2024)
- [Deep Time Series Models: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2407.13278/) (2024)
- [TimeFilter: Patch-Specific Spatial-Temporal Graph Filtration for Time Series Forecasting](https://mlsanity.com/paper/2501.13041/) (2025)
- [Generalizing Weather Forecast to Fine-grained Temporal Scales via Physics-AI Hybrid Modeling](https://mlsanity.com/paper/2405.13796/) (2024)
- [Weather2K: A Multivariate Spatio-Temporal Benchmark Dataset for Meteorological Forecasting Based on Real-Time Observation Data from Ground Weather Stations](https://mlsanity.com/paper/2302.10493/) (2023)
- [Physics-Guided Learning of Meteorological Dynamics for Weather Downscaling and Forecasting](https://mlsanity.com/paper/2505.14555/) (2025)

## Built on by (most cited first, 1 of 1)

- [M2Weather: A Benchmark for Joint Multi-Station and Multi-Variable Weather Forecasting](https://mlsanity.com/paper/2610.00370/) (2026)

## Abstract (arXiv)

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.