# Probabilistic Weather Forecasting with Hierarchical Graph Neural Networks

arXiv: https://arxiv.org/abs/2406.04759 · HTML: https://mlsanity.com/paper/2406.04759/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 50 references that are in the map.
- First posted on arXiv 7 Jun 2024.

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

- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [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)
- [GenCast: Diffusion-based ensemble forecasting for medium-range weather](https://mlsanity.com/paper/2312.15796/) (2023)
- [FengWu: Pushing the Skillful Global Medium-range Weather Forecast beyond 10 Days Lead](https://mlsanity.com/paper/2304.02948/) (2023)
- [Forecasting Global Weather with Graph Neural Networks](https://mlsanity.com/paper/2202.07575/) (2022)
- [Residual Corrective Diffusion Modeling for Km-scale Atmospheric Downscaling](https://mlsanity.com/paper/2309.15214/) (2023)
- [Scaling transformer neural networks for skillful and reliable medium-range weather forecasting](https://mlsanity.com/paper/2312.03876/) (2023)
- [Simulating Continuum Mechanics with Multi-Scale Graph Neural Networks](https://mlsanity.com/paper/2106.04900/) (2021)
- [AtmoRep: A stochastic model of atmosphere dynamics using large scale representation learning](https://mlsanity.com/paper/2308.13280/) (2023)
- [Uncertainty quantification for data-driven weather models](https://mlsanity.com/paper/2403.13458/) (2024)

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

- [OneForecast: A Universal Framework for Global and Regional Weather Forecasting](https://mlsanity.com/paper/2502.00338/) (2025)
- [Continuous Ensemble Weather Forecasting with Diffusion models](https://mlsanity.com/paper/2410.05431/) (2024)
- [Elucidated Rolling Diffusion Models for Probabilistic Forecasting of Complex Dynamics](https://mlsanity.com/paper/2506.20024/) (2025)
- [OmniCast: A Masked Latent Diffusion Model for Weather Forecasting Across Time Scales](https://mlsanity.com/paper/2510.18707/) (2025)
- [U-Cast: A Surprisingly Simple and Efficient Frontier Probabilistic AI Weather Forecaster](https://mlsanity.com/paper/2604.09041/) (2026)
- [Diffusion-LAM: Probabilistic Limited Area Weather Forecasting with Diffusion](https://mlsanity.com/paper/2502.07532/) (2025)
- [High-Resolution Probabilistic Data-Driven Weather Modeling with a Stretched-Grid](https://mlsanity.com/paper/2511.23043/) (2025)
- [ARROW: An Adaptive Rollout and Routing Method for Global Weather Forecasting](https://mlsanity.com/paper/2510.09734/) (2025)
- [FireCastNet: Earth-as-a-Graph for Seasonal Fire Prediction](https://mlsanity.com/paper/2502.01550/) (2025)
- [PEAR: Equal Area Weather Forecasting on the Sphere](https://mlsanity.com/paper/2505.17720/) (2025)
- [Regional Ocean Forecasting with Hierarchical Graph Neural Networks](https://mlsanity.com/paper/2410.11807/) (2024)
- [TCP-Diffusion: A Multi-modal Diffusion Model for Global Tropical Cyclone Precipitation Forecasting with Change Awareness](https://mlsanity.com/paper/2410.13175/) (2024)
- [Augmented Invertible Koopman Autoencoder for long-term time series forecasting](https://mlsanity.com/paper/2503.12930/) (2025)
- [Valid Error Bars for Neural Weather Models using Conformal Prediction](https://mlsanity.com/paper/2406.14483/) (2024)
- [Beyond Grid Data: Exploring Graph Neural Networks for Earth Observation](https://mlsanity.com/paper/2411.03223/) (2024)
- [Learning Stochastic Multiscale Models](https://mlsanity.com/paper/2506.22655/) (2025)
- [Assessing the Geographic Generalization and Physical Consistency of Generative Models for Climate Downscaling](https://mlsanity.com/paper/2510.13722/) (2025)
- [Tyche: One Step Flow for Efficient Probabilistic Weather Forecasting](https://mlsanity.com/paper/2605.06916/) (2026)
- [IndiaWeatherBench: A Dataset and Benchmark for Data-Driven Regional Weather Forecasting over India](https://mlsanity.com/paper/2509.00653/) (2025)
- [Graph-based Neural Space Weather Forecasting](https://mlsanity.com/paper/2509.19605/) (2025)
- [Hierarchical Graph Networks for Accurate Weather Forecasting via Lightweight Training](https://mlsanity.com/paper/2510.22094/) (2025)
- [Breaking Scale Anchoring: Frequency Representation Learning for Accurate High-Resolution Inference from Low-Resolution Training](https://mlsanity.com/paper/2512.05132/) (2025)
- [Reducing Smoothness with Expressive Memory Enhanced Hierarchical Graph Neural Networks](https://mlsanity.com/paper/2504.00349/) (2025)
- [On the use of Graphs for Satellite Image Time Series](https://mlsanity.com/paper/2505.16685/) (2025)
- [Fast and Flexible Probabilistic Forecasting of Dynamical Systems using Flow Matching and Physical Perturbation](https://mlsanity.com/paper/2508.01101/) (2025)
- [Deterministic and probabilistic neural surrogates of global hybrid-Vlasov simulations](https://mlsanity.com/paper/2601.12614/) (2026)
- [Ensemble Graph Neural Networks for Probabilistic Sea Surface Temperature Forecasting via Input Perturbations](https://mlsanity.com/paper/2603.06153/) (2026)
- [Stochastically Perturbed Weights: Ensembles from Deterministic Machine-Learning Weather Models](https://mlsanity.com/paper/2609.08412/) (2026)
- [Every Fixed Metric Has a Blind Spot: A Learned Atmospheric Critic for Scoring Forecast Realism](https://mlsanity.com/paper/2609.18381/) (2026)
- [Variational Augmented Invertible Koopman Autoencoder for probabilistic time series forecasting](https://mlsanity.com/paper/2609.37435/) (2026)

## Abstract (arXiv)

In recent years, machine learning has established itself as a powerful tool for high-resolution weather forecasting. While most current machine learning models focus on deterministic forecasts, accurately capturing the uncertainty in the chaotic weather system calls for probabilistic modeling. We propose a probabilistic weather forecasting model called Graph-EFM, combining a flexible latent-variable formulation with the successful graph-based forecasting framework. The use of a hierarchical graph construction allows for efficient sampling of spatially coherent forecasts. Requiring only a single forward pass per time step, Graph-EFM allows for fast generation of arbitrarily large ensembles. We experiment with the model on both global and limited area forecasting. Ensemble forecasts from Graph-EFM achieve equivalent or lower errors than comparable deterministic models, with the added benefit of accurately capturing forecast uncertainty.