# Huge Ensembles Part II: Properties of a Huge Ensemble of Hindcasts Generated with Spherical Fourier Neural Operators

arXiv: https://arxiv.org/abs/2408.01581 · HTML: https://mlsanity.com/paper/2408.01581/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 77 references that are in the map.
- First posted on arXiv 2 Aug 2024.

## Builds on (most cited first, 10 of 10)

- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [GenCast: Diffusion-based ensemble forecasting for medium-range weather](https://mlsanity.com/paper/2312.15796/) (2023)
- [Sub-seasonal forecasting with a large ensemble of deep-learning weather prediction models](https://mlsanity.com/paper/2102.05107/) (2021)
- [SwinVRNN: A Data-Driven Ensemble Forecasting Model via Learned Distribution Perturbation](https://mlsanity.com/paper/2205.13158/) (2022)
- [LUCIE: A Lightweight Uncoupled ClImate Emulator with long-term stability and physical consistency for O(1000)-member ensembles](https://mlsanity.com/paper/2405.16297/) (2024)
- [Dynamical Tests of a Deep-Learning Weather Prediction Model](https://mlsanity.com/paper/2309.10867/) (2023)
- [Forecaster's Dilemma: Extreme Events and Forecast Evaluation](https://mlsanity.com/paper/1512.09244/) (2015)
- [Neural Network Attribution Methods for Problems in Geoscience: A Novel Synthetic Benchmark Dataset](https://mlsanity.com/paper/2103.10005/) (2021)
- [FuXi-ENS: A machine learning model for medium-range ensemble weather forecasting](https://mlsanity.com/paper/2405.05925/) (2024)
- [Explaining the unexplainable: leveraging extremal dependence to characterize the 2021 Pacific Northwest heatwave](https://mlsanity.com/paper/2307.03688/) (2023)

## Built on by (most cited first, 12 of 12)

- [FourCastNet 3: A geometric approach to probabilistic machine-learning weather forecasting at scale](https://mlsanity.com/paper/2507.12144/) (2025)
- [Kilometer-Scale Convection Allowing Model Emulation using Generative Diffusion Modeling](https://mlsanity.com/paper/2408.10958/) (2024)
- [Can AI weather models predict out-of-distribution gray swan tropical cyclones?](https://mlsanity.com/paper/2410.14932/) (2024)
- [Huge Ensembles Part I: Design of Ensemble Weather Forecasts using Spherical Fourier Neural Operators](https://mlsanity.com/paper/2408.03100/) (2024)
- [Demystifying Data-Driven Probabilistic Medium-Range Weather Forecasting](https://mlsanity.com/paper/2601.18111/) (2026)
- [Community Research Earth Digital Intelligence Twin (CREDIT)](https://mlsanity.com/paper/2411.07814/) (2024)
- [Constructing Extreme Heatwave Storylines with Differentiable Climate Models](https://mlsanity.com/paper/2506.10660/) (2025)
- [Generalized Spherical Neural Operators: Green's Function Formulation](https://mlsanity.com/paper/2512.10723/) (2025)
- [MoWE : A Mixture of Weather Experts](https://mlsanity.com/paper/2509.09052/) (2025)
- [Geometric Laplace Neural Operator](https://mlsanity.com/paper/2512.16409/) (2025)
- [On the Predictive Skill of Artificial Intelligence-based Weather Models for Extreme Events using Uncertainty Quantification](https://mlsanity.com/paper/2511.17176/) (2025)
- [Neural Operators for Biomedical Spherical Heterogeneity](https://mlsanity.com/paper/2601.03561/) (2026)

## Abstract (arXiv)

In Part I, we created an ensemble based on Spherical Fourier Neural Operators. As initial condition perturbations, we used bred vectors, and as model perturbations, we used multiple checkpoints trained independently from scratch. Based on diagnostics that assess the ensemble's physical fidelity, our ensemble has comparable performance to operational weather forecasting systems. However, it requires orders of magnitude fewer computational resources. Here in Part II, we generate a huge ensemble (HENS), with 7,424 members initialized each day of summer 2023. We enumerate the technical requirements for running huge ensembles at this scale. HENS precisely samples the tails of the forecast distribution and presents a detailed sampling of internal variability. HENS has two primary applications: (1) as a large dataset with which to study the statistics and drivers of extreme weather and (2) as a weather forecasting system. For extreme climate statistics, HENS samples events 4σ away from the ensemble mean. At each grid cell, HENS increases the skill of the most accurate ensemble member and enhances coverage of possible future trajectories. As a weather forecasting model, HENS issues extreme weather forecasts with better uncertainty quantification. It also reduces the probability of outlier events, in which the verification value lies outside the ensemble forecast distribution.