提出新型球面神经网络Dandelion，专为行星动力学模拟设计。
Dandelion: A Spherical Flower for Neural Simulation of Planetary Dynamics
- 基于坐标变换（扭曲）实现球面特征传播，无传统卷积
- 在多个球面偏微分方程任务中表现最佳，高分辨率下优势更明显
- 适配气候、海洋等地球科学建模，适合需精确球面几何的场景
许多动力过程发生在球面上，但主流科学机器学习架构仍基于欧几里得空间。在经纬度网格上使用这些架构会引发问题：笛卡尔卷积在高纬度失真；二维FFT在傅里叶神经算子中错误假设双周期性；视觉变压器中的笛卡尔位置编码扭曲球面测地距离。近期工作开始采用原生球面基元，如球面卷积（DeepSphere或DISCO）、球面傅里叶神经算子（SFNO）和测地注意力。本文提出Dandelion，是Flower（一种基于扭曲的神经偏微分方程求解器）的球面版本。Dandelion各层预测切平面位移，并沿大圆传输特征。通过在球谐域内实现完全层级池化，构建类U-Net结构。因此无需卷积：空间混合仅通过球面坐标变换（即扭曲）实现。为评估Dandelion，我们发布一个动态演化的基准套件，包含多个具有挑战性的原生球面偏微分方程数据集，如修改版Galewsky急流、异常链式湍流、Cahn-Hilliard分解、球面黎曼激波、Held-Suarez干大气传输及全球海洋动力学。该基准填补了现有球面数据集的空白——既非过小而理想化，也非过大如ERA5导致模型迭代困难。Dandelion在所有数据集上均表现最优或第二优，且分辨率越高，与非扭曲基线的差距越大：在256×512分辨率下，Dandelion和Flower2D在单步预测与滚动预测中均占据前两名。
原文摘要 · Abstract (English)
Many dynamical processes unfold on the sphere but the default scientific machine learning architectures are Euclidean. Applying these architectures on a regular lat-lon grid causes problems: Cartesian convolutions become distorted at high latitude; 2D FFTs in Fourier neural operators incorrectly assume double periodicity; Cartesian positional encodings in ViTs distort spherical geodesic distances. Recent work moves towards natively spherical primitives, including spherical convolutions (e.g., DeepSphere or DISCO), Spherical Fourier Neural Operators (SFNOs), and geodesic attention. Here we propose Dandelion, a spherical version of Flower, a warp-based neural PDE solver. Layers of Dandelion predict a tangent-plane displacement and transport features along great circles. We obtain a U-Net-like structure by implementing hierarchical pooling entirely in the spherical-harmonic domain. There are thus no convolutions: spatial mixing is achieved only through spherical coordinate changes, or warps. To compare Dandelion with existing spherical architectures, we release an evolving benchmark suite of challenging, natively-spherical PDE datasets including a modified Galewsky jet, anomalous chained turbulence, Cahn-Hilliard decomposition, spherical Riemann shocks, Held-Suarez dry atmospheric transport and global ocean dynamics. This new benchmark fills the gap in existing spherical datasets which are either too small and stylized, or much too large (ERA5) for model iteration. Dandelion is best or second-best on every dataset, and the gap to non-warp baselines widens with resolution: at $256\times 512$, Dandelion and Flower2D occupy the top two slots in both single-step prediction and rollout.
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