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Dandelion: A Spherical Flower for Neural Simulation of Planetary Dynamics — arXiv:2608.27521

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.27521
License (as archived): CC0-1.0
Archived: 2026-10-17T11:06:22.158Z
SHA-256 of the archived text: 7b589e549050db4533e7f7f74a2e63ce5fc0b64c4007bc4a00bec28c802360e7
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How to cite

Dandelion: A Spherical Flower for Neural Simulation of Planetary Dynamics — arXiv:2608.27521 — arXiv (en), https://arxiv.org/abs/2608.27521 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_96ef3eaec9be (Metraipolis archive dc_96ef3eaec9be, sha256 7b589e549050db4533e7f7f74a2e63ce5fc0b64c4007bc4a00bec28c802360e7)

BibTeX

@misc{dc96ef3eaec9be,
  title = {Dandelion: A Spherical Flower for Neural Simulation of Planetary Dynamics — arXiv:2608.27521},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.27521},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_96ef3eaec9be; sha256 7b589e549050db4533e7f7f74a2e63ce5fc0b64c4007bc4a00bec28c802360e7},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.27521. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-08-31 in cs.LG).
Categorie arXiv: Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2608.27521 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T10:50:25.762Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-08-31?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).