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

TL;DR

UniPhy introduces a novel continuous-time, geometry-aware neural SPDE framework for planetary-scale weather modeling, capturing multi-scale dynamics and thermodynamic openness more accurately than traditional discrete models.

Contribution

It unifies Riemannian-Clifford geometry with biorthogonal spectral operators in a continuous-time neural SPDE, enabling physically consistent, adaptive, and computationally efficient weather simulations.

Findings

Achieves globally consistent operations via Riemannian-Clifford transformations.

Models transient energy growth with non-Hermitian biorthogonal spectral operators.

Reformulates physical integration as a parallel prefix-sum for efficiency.

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>.