Earth models test geometric data types for better predictions
Physically Typed and Geometry-Aware Representations for Earth Foundation Models
Computer Vision and Pattern RecognitionMachine Learning
Summary
Earth observation models are great at capturing complex geographic information, but they don’t always consider the special ways physical quantities behave on a spherical Earth. The authors suggest testing whether adding explicit geometric types—like vectors and tensors that change predictably with orientation—actually improves model accuracy. They propose a careful step-by-step evaluation comparing standard models with these geometry-aware versions on weather and climate data to see if the extra complexity helps. This approach avoids assuming more complex models are better without evidence.
What this means in practice
- •For weather modelers: Compare standard and geometry-aware data representations to improve accuracy in forecasting and climate simulations.
- •For remote sensing engineers: Design Earth observation models that explicitly encode physical field types to test if predictions improve under changing orientations or limited data.
A position paper. It proposes an approach and reports no results.
Authors
Rajiv Ranjan
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.