Eulerian-Lagrangian
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Biased sampling reduces particle settling velocities in turbidity currents
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Topology-Preserving Neural Operator Learning via Hodge Decomposition
arXiv:2605.13834v2 Announce Type: replace Abstract: 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 and operator splitting, we derive a...