mlsanityData to 14 Oct 2026

Postprocessing of Ensemble Weather Forecasts Using Permutation-invariant Neural Networks

arXiv 2309.04452 ↗First posted 8 Sep 2023stat.ML cs.LG physics.ao-phcited by 7

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Abstract (arXiv)

Statistical postprocessing is used to translate ensembles of raw numerical weather forecasts into reliable probabilistic forecast distributions. In this study, we examine the use of permutation-invariant neural networks for this task. In contrast to previous approaches, which often operate on ensemble summary statistics and dismiss details of the ensemble distribution, we propose networks that treat forecast ensembles as a set of unordered member forecasts and learn link functions that are by design invariant to permutations of the member ordering. We evaluate the quality of the obtained forecast distributions in terms of calibration and sharpness and compare the models against classical and neural network-based benchmark methods. In case studies addressing the postprocessing of surface temperature and wind gust forecasts, we demonstrate state-of-the-art prediction quality. To deepen the understanding of the learned inference process, we further propose a permutation-based importance analysis for ensemble-valued predictors, which highlights specific aspects of the ensemble forecast that are considered important by the trained postprocessing models. Our results suggest that most of the relevant information is contained in a few ensemble-internal degrees of freedom, which may impact the design of future ensemble forecasting and postprocessing systems.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 26 of its 67 references that are in the map. First posted on arXiv 8 Sep 2023.

Builds on

26 of 67 references.

References · 26

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14 more
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 3; 2025: 3; 2026: 1.

7 papers.

  1. 2025Learning Enhanced Ensemble Filterscited by 11
  2. 2024Graph Neural Networks and Spatial Information Learning for Post-Processing Ensemble Weather Forecastscited by 4
  3. 2024Valid Error Bars for Neural Weather Models using Conformal Predictioncited by 3
  4. 2024Self-attentive Transformer for Fast and Accurate Postprocessing of Temperature and Wind Speed Forecastscited by 2
  5. 2025Learning low-dimensional representations of ensemble forecast fields using autoencoder-based methodscited by 1
  6. 2026Attention Kernels for Learning Maps Between Heavy-Tailed Measurescited by 1
  7. 2025TLCCSP: A Scalable Framework for Enhancing Time Series Forecasting with Time-Lagged Cross-Correlationscited by 0