UniPhy: Unifying Riemannian-Clifford Geometry and Biorthogonal Dynamics for Planetary-Scale Continuous Weather Modeling
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908823322624000 |
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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 |