# Combining distribution-based neural networks to predict weather forecast probabilities

arXiv: https://arxiv.org/abs/2103.14430 · HTML: https://mlsanity.com/paper/2103.14430/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 38 references that are in the map.
- First posted on arXiv 26 Mar 2021.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [WeatherBench: A benchmark dataset for data-driven weather forecasting](https://mlsanity.com/paper/2002.00469/) (2020)
- [Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations](https://mlsanity.com/paper/1710.10121/) (2017)
- [Improving data-driven global weather prediction using deep convolutional neural networks on a cubed sphere](https://mlsanity.com/paper/2003.11927/) (2020)
- [Neural networks for post-processing ensemble weather forecasts](https://mlsanity.com/paper/1805.09091/) (2018)
- [Sub-seasonal forecasting with a large ensemble of deep-learning weather prediction models](https://mlsanity.com/paper/2102.05107/) (2021)
- [Deep Learning for Post-Processing Ensemble Weather Forecasts](https://mlsanity.com/paper/2005.08748/) (2020)
- [A generative adversarial network approach to (ensemble) weather prediction](https://mlsanity.com/paper/2006.07718/) (2020)

## Built on by (most cited first, 18 of 18)

- [WeatherBench 2: A benchmark for the next generation of data-driven global weather models](https://mlsanity.com/paper/2308.15560/) (2023)
- [Forecasting Global Weather with Graph Neural Networks](https://mlsanity.com/paper/2202.07575/) (2022)
- [Scaling transformer neural networks for skillful and reliable medium-range weather forecasting](https://mlsanity.com/paper/2312.03876/) (2023)
- [Probabilistic Forecasting with Generative Networks via Scoring Rule Minimization](https://mlsanity.com/paper/2112.08217/) (2021)
- [SwinVRNN: A Data-Driven Ensemble Forecasting Model via Learned Distribution Perturbation](https://mlsanity.com/paper/2205.13158/) (2022)
- [Generalizing Weather Forecast to Fine-grained Temporal Scales via Physics-AI Hybrid Modeling](https://mlsanity.com/paper/2405.13796/) (2024)
- [Explainable Artificial Intelligence for Bayesian Neural Networks: Towards trustworthy predictions of ocean dynamics](https://mlsanity.com/paper/2205.00202/) (2022)
- [Latent assimilation with implicit neural representations for unknown dynamics](https://mlsanity.com/paper/2309.09574/) (2023)
- [EWMoE: An effective model for global weather forecasting with mixture-of-experts](https://mlsanity.com/paper/2405.06004/) (2024)
- [AERIS: Argonne Earth Systems Model for Reliable and Skillful Predictions](https://mlsanity.com/paper/2509.13523/) (2025)
- [Aggregating distribution forecasts from deep ensembles](https://mlsanity.com/paper/2204.02291/) (2022)
- [Computing the ensemble spread from deterministic weather predictions using conditional generative adversarial networks](https://mlsanity.com/paper/2205.09182/) (2022)
- [Defining error accumulation in ML atmospheric simulators](https://mlsanity.com/paper/2405.14714/) (2024)
- [Distilling Machine Learning's Added Value: Pareto Fronts in Atmospheric Applications](https://mlsanity.com/paper/2408.02161/) (2024)
- [Decomposing weather forecasting into advection and convection with neural networks](https://mlsanity.com/paper/2405.06590/) (2024)
- [Bayesian neural networks for the probabilistic forecasting of wind direction and speed using ocean data](https://mlsanity.com/paper/2206.08953/) (2022)
- [Towards replacing precipitation ensemble predictions systems using machine learning](https://mlsanity.com/paper/2304.10251/) (2023)
- [Learning to simulate partially known spatio-temporal dynamics with trainable difference operators](https://mlsanity.com/paper/2307.14395/) (2023)

## Abstract (arXiv)

The success of deep learning techniques over the last decades has opened up a new avenue of research for weather forecasting. Here, we take the novel approach of using a neural network to predict full probability density functions at each point in space and time rather than a single output value, thus producing a probabilistic weather forecast. This enables the calculation of both uncertainty and skill metrics for the neural network predictions, and overcomes the common difficulty of inferring uncertainty from these predictions. This approach is data-driven and the neural network is trained on the WeatherBench dataset (processed ERA5 data) to forecast geopotential and temperature 3 and 5 days ahead. Data exploration leads to the identification of the most important input variables, which are also found to agree with physical reasoning, thereby validating our approach. In order to increase computational efficiency further, each neural network is trained on a small subset of these variables. The outputs are then combined through a stacked neural network, the first time such a technique has been applied to weather data. Our approach is found to be more accurate than some numerical weather prediction models and as accurate as more complex alternative neural networks, with the added benefit of providing key probabilistic information necessary for making informed weather forecasts.