发表机构
Plaksha University（普拉沙大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过分阶段证伪程序，在ERA5预演中比较传统与几何类型化嵌入，探究地球基础模型是否应显式保留物理场变换规律，以验证其能否带来可复现的实际改进。
AI 中文摘要
地球观测（EO）基础模型在学习语义性、高维地理空间嵌入方面已变得极为有效，而现代天气与气候模型则证明，地球特有的几何结构、球面算子、网格以及混合物理求解器能够显著改善预测。然而，这两类进展并不等价。传统的潜在嵌入不具备固有的物理变换规律，而标量场、切向极向量场、轴向量/赝矢量量、余向量以及高阶张量在旋转、反射及局部坐标系变化下具有不同的变换方式。本研究提出一个问题：通用地球基础模型是否应明确保留这些区分，还是标准嵌入加数据增强已足以学习所有重要信息。因此，核心贡献并非基于假设采用更复杂的架构，而是分阶段的证伪程序。首先，在计算受限的ERA5预演中，比较传统、增强匹配、类型化等变以及Hodge/Helmholtz变体在空间、时间、方向和低数据偏移下的表现。仅当显式几何类型化产生可复现的改进时，该程序才推进至多模态地球基础模型，使语义嵌入与物理类型化场共存。所提出的差距比声称现有模型完全忽略几何更窄且更具说服力：若干系统已尊重球面域几何，新兴工作明确学习球面上的标量/向量场。未解决的问题是，基础模型规模、多模态、宇称感知的场类型化是否能在这些现有方法之外产生实际收益。
英文摘要
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.
Comments18 pages
