UniPhy: Unifying Riemannian-Clifford Geometry and Biorthogonal Dynamics for Planetary-Scale Continuous Weather Modeling
Ruiqing Yan, Haoyu Deng, Yuhang Shao, Xingbo Du, Jingyuan Wang, Zhengyi Yang
RAIDS Lab Authors
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Abstract
While data-driven weather models have achieved remarkable deterministic accuracy, they fundamentally rely on discrete-time mappings and closed-system assumptions, failing to capture the multi-scale continuous dynamics and thermodynamic openness of the atmosphere. To address these limitations, we propose UniPhy, a continuous-time non-Hermitian neural stochastic partial differential equation (SPDE) solver. Geometrically, we employ Riemannian-Clifford gauge transformations to flatten planetary heterogeneity, enabling globally consistent operations. Dynamically, we construct non-Hermitian biorthogonal spectral operators integrated with a global flux tracker to capture transient energy growth and open-system exchange. Computationally, by identifying the algebraic associativity of the analytic solution, we reformulate adaptive physical integration as a parallel prefix-sum problem, achieving log-linear sequence parallelism. UniPhy establishes a physically complete foundation model architecture that unifies geometric adaptivity, thermodynamic consistency, and computational efficiency. Our code is available at https://github.com/yrqUni/UniPhy.
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BibTeX
@misc{yan2026uniphy,
title = {UniPhy: Unifying Riemannian-Clifford Geometry and Biorthogonal Dynamics for Planetary-Scale Continuous Weather Modeling},
author = {Ruiqing Yan and Haoyu Deng and Yuhang Shao and Xingbo Du and Jingyuan Wang and Zhengyi Yang},
year = {2026},
eprint = {2602.09030},
archivePrefix = {arXiv},
primaryClass = {physics.comp-ph},
url = {https://arxiv.org/abs/2602.09030}
}