**摘要**
In this paper, we study solution operators of physical field equations on geometric meshes from a function-space perspective. We reveal that Hodge orthogonality fundamentally resolves spectral interference by isolating unlearnable topological degrees of freedom from learnable geometric dynamics, enabling an additive approximation confined to structure-preserving subspaces. Building on Hodge theory
👤 作者: Dongzhe Zheng, Tao Zhong, Christine Allen-Blanchette

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🔗 **[通过Hodge分解保持拓扑结构的神经算子学习](https://arxiv.org/abs/2605.13834v1)**

> Topology-Preserving Neural Operator Learning via Hodge Decomposition
🏷️ 来源: ArXiv cs.AI
⏱️ 2026-05-15 08:00