Dandelion: A Spherical Flower for Neural Simulation of Planetary Dynamics
Dandelion is a natively spherical neural PDE solver that adapts the Flower architecture for spherical domains, using tangent-plane displacement prediction and feature transport along great circles instead of convolutions Hierarchical pooling is implemented entirely in the spherical-harmonic domain, producing a U-Net-like structure without any convolutional operations The authors release an evolving benchmark suite of natively-spherical PDE datasets (Galewsky jet, chained turbulence, Cahn-Hilliar
Analysis
TL;DR
- Dandelion is a natively spherical neural PDE solver that adapts the Flower architecture for spherical domains, using tangent-plane displacement prediction and feature transport along great circles instead of convolutions
- Hierarchical pooling is implemented entirely in the spherical-harmonic domain, producing a U-Net-like structure without any convolutional operations
- The authors release an evolving benchmark suite of natively-spherical PDE datasets (Galewsky jet, chained turbulence, Cahn-Hilliard decomposition, Riemann shocks, Held-Suarez atmospheric transport, global ocean dynamics) that fills the gap between overly small/stylized and excessively large (ERA5) datasets
- Dandelion achieves best or second-best results across all benchmark datasets, with performance gaps over non-warp baselines widening at higher resolutions (256×512)
Why It Matters
This work addresses a critical limitation in scientific machine learning: most architectures are Euclidean-by-default and suffer from geometric distortions when applied to spherical domains like planetary atmospheres and oceans. Dandelion provides a principled, convolution-free alternative that respects the intrinsic geometry of the sphere, making it directly relevant for climate modeling, weather prediction, and geophysical fluid dynamics.
Technical Details
- Dandelion layers predict tangent-plane displacements and transport features along great circles, avoiding the high-latitude distortion problems inherent to Cartesian convolutions on lat-lon grids
- Spatial mixing is achieved exclusively through spherical coordinate changes (warps), eliminating convolutions entirely; hierarchical U-Net-like structure is realized via spherical-harmonic domain pooling
- The benchmark suite includes six challenging PDE datasets: modified Galewsky jet, anomalous chained turbulence, Cahn-Hilliard decomposition, spherical Riemann shocks, Held-Suarez dry atmospheric transport, and global ocean dynamics
- At 256×512 resolution, Dandelion and its 2D counterpart Flower2D occupy the top two slots in both single-step prediction and long rollout evaluations, with the performance gap over non-warp baselines increasing with resolution
Industry Insight
- The warp-based approach offers a compelling alternative to spherical convolutions and Fourier-based operators, suggesting that coordinate-transport mechanisms may generalize to other non-Euclidean manifolds beyond the sphere
- The released benchmark suite addresses a real infrastructure gap in the community, enabling faster model iteration for geophysical ML without the computational burden of full-scale reanalysis data like ERA5
- As spherical PDE solvers become more competitive with traditional numerical methods, expect increased adoption in operational weather and climate modeling pipelines, particularly for medium-range forecasting and Earth system model emulation
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