UniPhy: Unifying Riemannian-Clifford Geometry and Biorthogonal Dynamics for Planetary-Scale Continuous Weather Modeling

Fuente: arXiv
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Autori principali: Yan, Ruiqing, Deng, Haoyu, Shao, Yuhang, Du, Xingbo, Wang, Jingyuan, Yang, Zhengyi
Natura: Preprint
Pubblicazione: 2026
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author Yan, Ruiqing
Deng, Haoyu
Shao, Yuhang
Du, Xingbo
Wang, Jingyuan
Yang, Zhengyi
author_facet Yan, Ruiqing
Deng, Haoyu
Shao, Yuhang
Du, Xingbo
Wang, Jingyuan
Yang, Zhengyi
contents 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>.
format Preprint
id arxiv_https___arxiv_org_abs_2602_09030
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle UniPhy: Unifying Riemannian-Clifford Geometry and Biorthogonal Dynamics for Planetary-Scale Continuous Weather Modeling
Yan, Ruiqing
Deng, Haoyu
Shao, Yuhang
Du, Xingbo
Wang, Jingyuan
Yang, Zhengyi
Computational Physics
Atmospheric and Oceanic Physics
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>.
title UniPhy: Unifying Riemannian-Clifford Geometry and Biorthogonal Dynamics for Planetary-Scale Continuous Weather Modeling
topic Computational Physics
Atmospheric and Oceanic Physics
url https://arxiv.org/abs/2602.09030