Dandelion: A Spherical Flower for Neural Simulation of Planetary Dynamics
arXiv:2608.27521v1 Announce Type: new Abstract: 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.
-->
[Submitted on 27 Aug 2026]
Title:Dandelion: A Spherical Flower for Neural Simulation of Planetary Dynamics
View a PDF of the paper titled Dandelion: A Spherical Flower for Neural Simulation of Planetary Dynamics, by Till Muser and 1 other authors
View PDF HTML (experimental)
Abstract: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.
Subjects:
Machine Learning (cs.LG)
Cite as: arXiv:2608.27521 [cs.LG]
(or arXiv:2608.27521v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2608.27521
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Till Muser [view email] [v1] Thu, 27 Aug 2026 12:43:03 UTC (21,324 KB)
Full-text links:
Access Paper:
View a PDF of the paper titled Dandelion: A Spherical Flower for Neural Simulation of Planetary Dynamics, by Till Muser and 1 other authors
View PDF
HTML (experimental)
TeX Source
view license
Current browse context:
cs.LG
new | recent | 2026-08
Change to browse by:
cs
References & Citations
NASA ADS
Google Scholar
Semantic Scholar
Loading...
Data provided by:
Bibliographic Tools
Bibliographic and Citation Tools
Bibliographic Explorer Toggle
Bibliographic Explorer (What is the Explorer?)
Connected Papers Toggle
Connected Papers (What is Connected Papers?)
Litmaps Toggle
Litmaps (What is Litmaps?)
scite.ai Toggle
scite Smart Citations (What are Smart Citations?)
Code, Data, Media
Code, Data and Media Associated with this Article
alphaXiv Toggle
alphaXiv (What is alphaXiv?)
Links to Code Toggle
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub Toggle
DagsHub (What is DagsHub?)
GotitPub Toggle
Gotit.pub (What is GotitPub?)
Huggingface Toggle
Hugging Face (What is Huggingface?)
ScienceCast Toggle
ScienceCast (What is ScienceCast?)
Demos
Demos
Replicate Toggle
Replicate (What is Replicate?)
Spaces Toggle
Hugging Face Spaces (What is Spaces?)
Spaces Toggle
TXYZ.AI (What is TXYZ.AI?)
Related Papers
Recommenders and Search Tools
Link to Influence Flower
Influence Flower (What are Influence Flowers?)
Core recommender toggle
CORE Recommender (What is CORE?)
IArxiv recommender toggle
IArxiv Recommender (What is IArxiv?)
Author
Venue
Institution
Topic
About arXivLabs
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)