# Neural networks for post-processing ensemble weather forecasts

arXiv: https://arxiv.org/abs/1805.09091 · HTML: https://mlsanity.com/paper/1805.09091/

## Key facts

- Cited by 95 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2018.

## Built on by (most cited first, 30 of 95)

- [Neural General Circulation Models for Weather and Climate](https://mlsanity.com/paper/2311.07222/) (2023)
- [WeatherBench 2: A benchmark for the next generation of data-driven global weather models](https://mlsanity.com/paper/2308.15560/) (2023)
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- [FourCastNet 3: A geometric approach to probabilistic machine-learning weather forecasting at scale](https://mlsanity.com/paper/2507.12144/) (2025)
- [AtmoRep: A stochastic model of atmosphere dynamics using large scale representation learning](https://mlsanity.com/paper/2308.13280/) (2023)
- [Machine learning methods for postprocessing ensemble forecasts of wind gusts: A systematic comparison](https://mlsanity.com/paper/2106.09512/) (2021)
- [Forecast combinations: an over 50-year review](https://mlsanity.com/paper/2205.04216/) (2022)
- [Physically Constrained Generative Adversarial Networks for Improving Precipitation Fields from Earth System Models](https://mlsanity.com/paper/2209.07568/) (2022)
- [Generative machine learning methods for multivariate ensemble post-processing](https://mlsanity.com/paper/2211.01345/) (2022)
- [Uncertainty quantification for data-driven weather models](https://mlsanity.com/paper/2403.13458/) (2024)
- [Flexible Model Aggregation for Quantile Regression](https://mlsanity.com/paper/2103.00083/) (2021)
- [Climate Modeling with Neural Diffusion Equations](https://mlsanity.com/paper/2111.06011/) (2021)
- [Skillful Twelve Hour Precipitation Forecasts using Large Context Neural Networks](https://mlsanity.com/paper/2111.07470/) (2021)
- [ExtremeCast: Boosting Extreme Value Prediction for Global Weather Forecast](https://mlsanity.com/paper/2402.01295/) (2024)
- [Combining distribution-based neural networks to predict weather forecast probabilities](https://mlsanity.com/paper/2103.14430/) (2021)
- [Probabilistic neural operators for functional uncertainty quantification](https://mlsanity.com/paper/2502.12902/) (2025)
- [WeatherBench Probability: A benchmark dataset for probabilistic medium-range weather forecasting along with deep learning baseline models](https://mlsanity.com/paper/2205.00865/) (2022)
- [Bridging observation, theory and numerical simulation of the ocean using Machine Learning](https://mlsanity.com/paper/2104.12506/) (2021)
- [Comparing Explanation Methods for Traditional Machine Learning Models Part 1: An Overview of Current Methods and Quantifying Their Disagreement](https://mlsanity.com/paper/2211.08943/) (2022)
- [Spatial Mixture-of-Experts](https://mlsanity.com/paper/2211.13491/) (2022)
- [ENS-10: A Dataset For Post-Processing Ensemble Weather Forecasts](https://mlsanity.com/paper/2206.14786/) (2022)
- [Do AI models produce better weather forecasts than physics-based models? A quantitative evaluation case study of Storm Ciar'an](https://mlsanity.com/paper/2312.02658/) (2023)
- [Evidential Deep Learning: Enhancing Predictive Uncertainty Estimation for Earth System Science Applications](https://mlsanity.com/paper/2309.13207/) (2023)
- [An Axiomatic Assessment of Entropy- and Variance-based Uncertainty Quantification in Regression](https://mlsanity.com/paper/2504.18433/) (2025)
- [End-to-End Probabilistic Framework for Learning with Hard Constraints](https://mlsanity.com/paper/2506.07003/) (2025)
- [UTOPIA: Universally Trainable Optimal Prediction Intervals Aggregation](https://mlsanity.com/paper/2306.16549/) (2023)
- [Self-Attentive Ensemble Transformer: Representing Ensemble Interactions in Neural Networks for Earth System Models](https://mlsanity.com/paper/2106.13924/) (2021)
- [Evaluation of Machine Learning Techniques for Forecast Uncertainty Quantification](https://mlsanity.com/paper/2111.14844/) (2021)
- [Postprocessing of Ensemble Weather Forecasts Using Permutation-invariant Neural Networks](https://mlsanity.com/paper/2309.04452/) (2023)
- [Postprocessing of point predictions for probabilistic forecasting of day-ahead electricity prices: The benefits of using isotonic distributional regression](https://mlsanity.com/paper/2404.02270/) (2024)

## Abstract (arXiv)

Ensemble weather predictions require statistical post-processing of systematic errors to obtain reliable and accurate probabilistic forecasts. Traditionally, this is accomplished with distributional regression models in which the parameters of a predictive distribution are estimated from a training period. We propose a flexible alternative based on neural networks that can incorporate nonlinear relationships between arbitrary predictor variables and forecast distribution parameters that are automatically learned in a data-driven way rather than requiring pre-specified link functions. In a case study of 2-meter temperature forecasts at surface stations in Germany, the neural network approach significantly outperforms benchmark post-processing methods while being computationally more affordable. Key components to this improvement are the use of auxiliary predictor variables and station-specific information with the help of embeddings. Furthermore, the trained neural network can be used to gain insight into the importance of meteorological variables thereby challenging the notion of neural networks as uninterpretable black boxes. Our approach can easily be extended to other statistical post-processing and forecasting problems. We anticipate that recent advances in deep learning combined with the ever-increasing amounts of model and observation data will transform the post-processing of numerical weather forecasts in the coming decade.