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This paper proposes a rigorous, compute-conscious evaluation of whether Earth foundation models should explicitly encode physical geometric distinctions (such as scalar vs. vector fields) or if standard augmented embeddings suffice. Rather than assuming complexity is beneficial, the authors advocate for a staged falsification program to determine if physically typed representations yield reproducible gains over conventional approaches in spatial and temporal tasks. The core contribution lies in bridging the gap between semantic geospatial embeddings and physics-aware modeling through empirical validation rather than architectural assumption.
Physically Typed and Geometry-Aware Representations for Earth Foundation Models
arXiv:2609.13868v1 Announce Type: cross 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.
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.
Computer Vision and Pattern Recognition (cs.CV); Machine Learning (cs.LG)
arXiv:2609.13868 [cs.CV]
(or arXiv:2609.13868v1 [cs.CV] for this version)
https://doi.org/10.48550/arXiv.2609.13868 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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