# Graph Neural Networks and Spatial Information Learning for Post-Processing Ensemble Weather Forecasts

arXiv: https://arxiv.org/abs/2407.11050 · HTML: https://mlsanity.com/paper/2407.11050/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 30 references that are in the map.
- First posted on arXiv 8 Jul 2024.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [Spatial-Temporal Fusion Graph Neural Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2012.09641/) (2020)
- [Neural networks for post-processing ensemble weather forecasts](https://mlsanity.com/paper/1805.09091/) (2018)
- [Machine learning methods for postprocessing ensemble forecasts of wind gusts: A systematic comparison](https://mlsanity.com/paper/2106.09512/) (2021)
- [Generative machine learning methods for multivariate ensemble post-processing](https://mlsanity.com/paper/2211.01345/) (2022)
- [Postprocessing of Ensemble Weather Forecasts Using Permutation-invariant Neural Networks](https://mlsanity.com/paper/2309.04452/) (2023)

## Built on by (most cited first, 4 of 4)

- [A Composite-Loss Graph Neural Network for the Multivariate Post-Processing of Ensemble Weather Forecasts](https://mlsanity.com/paper/2509.02784/) (2025)
- [STIPP: Space-time in situ postprocessing over the French Alps using proper scoring rules](https://mlsanity.com/paper/2601.02882/) (2026)
- [Statistical versus machine learning-based spatial interpolation of post-processed ensemble weather forecasts](https://mlsanity.com/paper/2609.07512/) (2026)
- [SCORE: Spectral Correlation Estimation for Multivariate Gaussians](https://mlsanity.com/paper/2610.12096/) (2026)

## Abstract (arXiv)

Ensemble forecasts from numerical weather prediction models show systematic errors that require correction via post-processing. While there has been substantial progress in flexible neural network-based post-processing methods over the past years, most station-based approaches still treat every input data point separately which limits the capabilities for leveraging spatial structures in the forecast errors. In order to improve information sharing across locations, we propose a graph neural network architecture for ensemble post-processing, which represents the station locations as nodes on a graph and utilizes an attention mechanism to identify relevant predictive information from neighboring locations. In a case study on 2-m temperature forecasts over Europe, the graph neural network model shows substantial improvements over a highly competitive neural network-based post-processing method.