Hodge Spectral Duality provides a topology-preserving neural operator by isolating unlearnable topological components via Hodge orthogonality and operator splitting.
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Interprets splitting schemes as Dirac-controlled trajectories to prove arbitrary-order complex schemes exist and to tie real-order restrictions to obstructing Lie brackets.
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Topology-Preserving Neural Operator Learning via Hodge Decomposition
Hodge Spectral Duality provides a topology-preserving neural operator by isolating unlearnable topological components via Hodge orthogonality and operator splitting.
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Control theory and splitting methods
Interprets splitting schemes as Dirac-controlled trajectories to prove arbitrary-order complex schemes exist and to tie real-order restrictions to obstructing Lie brackets.