# S3N: A Spherical Spiral Scanning Network for Weather Forecasting

arXiv: https://arxiv.org/abs/2610.04338 · HTML: https://mlsanity.com/paper/2610.04338/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 31 references that are in the map.
- First posted on arXiv 3 Oct 2026.

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

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [VMamba: Visual State Space Model](https://mlsanity.com/paper/2401.10166/) (2024)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [ClimaX: A foundation model for weather and climate](https://mlsanity.com/paper/2301.10343/) (2023)
- [FuXi: A cascade machine learning forecasting system for 15-day global weather forecast](https://mlsanity.com/paper/2306.12873/) (2023)
- [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)
- [Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere](https://mlsanity.com/paper/2306.03838/) (2023)
- [FengWu: Pushing the Skillful Global Medium-range Weather Forecast beyond 10 Days Lead](https://mlsanity.com/paper/2304.02948/) (2023)
- [Scaling transformer neural networks for skillful and reliable medium-range weather forecasting](https://mlsanity.com/paper/2312.03876/) (2023)
- [DeepSphere: Efficient spherical Convolutional Neural Network with HEALPix sampling for cosmological applications](https://mlsanity.com/paper/1810.12186/) (2018)
- [OneForecast: A Universal Framework for Global and Regional Weather Forecasting](https://mlsanity.com/paper/2502.00338/) (2025)
- [Advancing Parsimonious Deep Learning Weather Prediction using the HEALPix Mesh](https://mlsanity.com/paper/2311.06253/) (2023)
- [HEAL-SWIN: A Vision Transformer On The Sphere](https://mlsanity.com/paper/2307.07313/) (2023)
- [HEAL-ViT: Vision Transformers on a spherical mesh for medium-range weather forecasting](https://mlsanity.com/paper/2403.17016/) (2024)
- [OSLO: On-the-Sphere Learning for Omnidirectional images and its application to 360-degree image compression](https://mlsanity.com/paper/2107.09179/) (2021)
- [PEAR: Equal Area Weather Forecasting on the Sphere](https://mlsanity.com/paper/2505.17720/) (2025)

## Abstract (arXiv)

Machine learning-based weather prediction (MLWP) has achieved strong performance in global weather forecasting. Recent Hierarchical Equal Area isoLatitude Pixelation (HEALPix)-based methods use the HEALPix (HP) grid to avoid area distortion near the poles of conventional latitude-longitude (LL) grids. However, existing HP-based approaches often use pointwise mapping methods and process HP pixels within separate base faces or local windows. Consequently, the mapping may introduce reconstruction errors and cross-face communication depends on handcrafted boundary handling or shifted windows. We propose the Spherical Spiral Scanning Network (S3N) to address both limitations. First, L2Proj provides a bidirectional method for mapping atmospheric fields between the LL and HP grids through an L2 projection of their continuous finite-element representations. Second, the Attention-Guided Quad-Spiral State-Space Scanning (AQSS) block uses cross-latitude attention to guide selective state-space updates along four global pole-to-pole spiral paths. This design enables continuous information propagation across HP base-face boundaries without additional boundary-processing mechanisms. Experiments show that S3N achieves better results at 4-, 7-, and 10-day lead times, and exhibits slower error growth in long-range forecasting.