Dandelion Neural Network Simulates Planetary Dynamics on Sphere

This paper introduces Dandelion, a novel neural PDE solver specifically engineered for simulating dynamical processes that occur on a spherical surface, such as those found in planetary science and climate modeling. Traditional scientific machine learning architectures, which are often Euclidean, struggle with spherical data due to distortions at high latitudes, incorrect periodicity assumptions, and inaccurate geodesic distance representations. Dandelion addresses these issues by adopting natively spherical primitives. It is a spherical adaptation of the warp-based Flower solver, featuring layers that predict tangent-plane displacements and transport features along great circles. Its U-Net-like structure implements hierarchical pooling entirely within the spherical-harmonic domain, eliminating the need for convolutions and achieving spatial mixing through spherical coordinate changes. Evaluated against a new benchmark suite of challenging spherical PDE datasets, Dandelion consistently performs as the best or second-best model, with its advantage growing significantly at higher resolutions.