Physically Typed and Geometry-Aware Representations for Earth Foundation Models

2026-09-12

AI Summary

研究探讨了地球基础模型中物理类型化和几何感知表示的必要性，通过对比不同方法在多种条件下的表现，验证其是否能带来实质性改进。

Abstract

Earth-observation (EO) foundation models have become exceptionally effective at learning se mantic, high-dimensional geospatial embeddings, while modern weather and climate models have demonstrated that Earth-specific geometry, spherical operators, meshes, and hybrid physical solvers can materially improve prediction. Yet these two advances are not equivalent. A conventional latent embedding has no inherent physical transformation law, whereas scalar fields, tangent polar-vector fields, axial/pseudovector quantities, covectors, and higher-order tensors transform differently under rotations, reflections, and changes of local coordinate frame. This proposal asks whether a general purpose Earth foundation model should preserve those distinctions explicitly, or whether standard embeddings plus augmentation already learn everything that matters. The central contribution is therefore not a more complicated architecture by assumption, but a staged falsification program. A compute-conscious ERA5 dry run first compares conventional, augmentation-matched, typed equivariant, and Hodge/Helmholtz variants under spatial, temporal, orientation, and low-data shifts. Only if explicit geometric typing yields reproducible improvements does the program advance toward a multimodal Earth foundation model in which semantic embeddings coexist with physically typed fields. The proposed gap is narrower and more defensible than claiming that current models ignore geometry entirely: several systems already respect spherical domain geometry, and emerging work explicitly learns scalar/vector fields on spheres. The unresolved question is whether foundation-scale, multimodal, parity-aware field typing produces practical gains beyond those existing approaches.

Problem

• Earth foundation model
• physical transformation
• geometric typing

Innovation

• physically typed fields
• geometry-aware representations
• equivariant
• multimodal Earth foundation model
• Hodge/Helmholtz