Raw finite-query preorders collapse the CH23 spectral block to a single source while modal preorders under geometric admissibility yield exactly two minimal exact sources, reformulating the SCI exact-basis problem.
Convergent methods for koopman operators on reproducing kernel hilbert spaces
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DeepMDMD combines deep latent embedding with an exact multiplicative DMD constraint to learn compact, algebra-preserving dictionaries for nonlinear dynamics.
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Finite-Query Collapse and Modal Exact Bases in the SCI Hierarchy
Raw finite-query preorders collapse the CH23 spectral block to a single source while modal preorders under geometric admissibility yield exactly two minimal exact sources, reformulating the SCI exact-basis problem.
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Deep Embedded Multiplicative DMD for Algebra-Preserving Koopman Learning
DeepMDMD combines deep latent embedding with an exact multiplicative DMD constraint to learn compact, algebra-preserving dictionaries for nonlinear dynamics.