# FuXi-ENS: A machine learning model for medium-range ensemble weather forecasting

arXiv: https://arxiv.org/abs/2405.05925 · HTML: https://mlsanity.com/paper/2405.05925/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 95 references that are in the map.
- First posted on arXiv 9 May 2024.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [WeatherBench: A benchmark dataset for data-driven weather forecasting](https://mlsanity.com/paper/2002.00469/) (2020)
- [FuXi: A cascade machine learning forecasting system for 15-day global weather forecast](https://mlsanity.com/paper/2306.12873/) (2023)
- [WeatherBench 2: A benchmark for the next generation of data-driven global weather models](https://mlsanity.com/paper/2308.15560/) (2023)
- [Learning Discourse-level Diversity for Neural Dialog Models using Conditional Variational Autoencoders](https://mlsanity.com/paper/1703.10960/) (2017)
- [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)
- [SwinVRNN: A Data-Driven Ensemble Forecasting Model via Learned Distribution Perturbation](https://mlsanity.com/paper/2205.13158/) (2022)
- [A Practical Probabilistic Benchmark for AI Weather Models](https://mlsanity.com/paper/2401.15305/) (2024)
- [FuXi-Extreme: Improving extreme rainfall and wind forecasts with diffusion model](https://mlsanity.com/paper/2310.19822/) (2023)

## Built on by (most cited first, 13 of 13)

- [Continuous Ensemble Weather Forecasting with Diffusion models](https://mlsanity.com/paper/2410.05431/) (2024)
- [FuXi Weather: A data-to-forecast machine learning system for global weather](https://mlsanity.com/paper/2408.05472/) (2024)
- [Huge Ensembles Part I: Design of Ensemble Weather Forecasts using Spherical Fourier Neural Operators](https://mlsanity.com/paper/2408.03100/) (2024)
- [Huge Ensembles Part II: Properties of a Huge Ensemble of Hindcasts Generated with Spherical Fourier Neural Operators](https://mlsanity.com/paper/2408.01581/) (2024)
- [Modulated Adaptive Fourier Neural Operators for Temporal Interpolation of Weather Forecasts](https://mlsanity.com/paper/2410.18904/) (2024)
- [Data-driven ensemble prediction of the global ocean](https://mlsanity.com/paper/2603.19591/) (2026)
- [Learning low-dimensional representations of ensemble forecast fields using autoencoder-based methods](https://mlsanity.com/paper/2502.04409/) (2025)
- [CSU-PCAST: A Dual-Branch Transformer Framework for medium-range ensemble Precipitation Forecasting](https://mlsanity.com/paper/2510.20769/) (2025)
- [Probabilistic Transformers for Joint Modeling of Global Weather Dynamics and Decision-Centric Variables](https://mlsanity.com/paper/2601.03753/) (2026)
- [Quantile Regression, Variational Autoencoders, and Diffusion Models for Uncertainty Quantification: A Spatial Analysis of Sub-seasonal Wind Speed Prediction](https://mlsanity.com/paper/2510.16958/) (2025)
- [Revealing the Potential of Learnable Perturbation Ensemble Forecast Model for Tropical Cyclone Prediction](https://mlsanity.com/paper/2510.23794/) (2025)
- [A Synergistic Approach: Dynamics-AI Ensemble in Tropical Cyclone Forecasting](https://mlsanity.com/paper/2602.22533/) (2026)
- [Neptune: An AI model for Global Ocean Subseasonal Prediction](https://mlsanity.com/paper/2609.08606/) (2026)

## Abstract (arXiv)

Ensemble forecasting is crucial for improving weather predictions, especially for forecasts of extreme events. Constructing an ensemble prediction system (EPS) based on conventional NWP models is highly computationally expensive. ML models have emerged as valuable tools for deterministic weather forecasts, providing forecasts with significantly reduced computational requirements and even surpassing the forecast performance of traditional NWP models. However, challenges arise when applying ML models to ensemble forecasting. Recent ML models, such as GenCast and SEEDS model, rely on the ERA5 EDA or operational NWP ensemble members for forecast generation. Their spatial resolution is also considered too coarse for many applications. To overcome these limitations, we introduce FuXi-ENS, an advanced ML model designed to deliver 6-hourly global ensemble weather forecasts up to 15 days. This model runs at a significantly increased spatial resolution of 0.25textdegree, incorporating 5 atmospheric variables at 13 pressure levels, along with 13 surface variables. By leveraging the inherent probabilistic nature of Variational AutoEncoder (VAE), FuXi-ENS optimizes a loss function that combines the CRPS and the KL divergence between the predicted and target distribution, facilitating the incorporation of flow-dependent perturbations in both initial conditions and forecast. This innovative approach makes FuXi-ENS an advancement over the traditional ones that use L1 loss combined with the KL loss in standard VAE models for ensemble weather forecasting. Results demonstrate that FuXi-ENS outperforms ensemble forecasts from the ECMWF, a world leading NWP model, in the CRPS of 98.1% of 360 variable and forecast lead time combinations. This achievement underscores the potential of the FuXi-ENS model to enhance ensemble weather forecasts, offering a promising direction for further development in this field.