koopman-generator
Koopman operator theory for infinite-dimensional linear lifting of nonlinear dynamics. Generates dynamics from observables.
npx skills add majiayu000/claude-skill-registry --skill koopman-generator --agent claude-code
Same command for any agent — swap --agent for codex, cursor, copilot.
Weekly change comes from our own snapshots, not the repository page — it measures attention, not adoption.
# Koopman Generator Skill ## Core Idea The **Koopman operator** K linearizes nonlinear dynamics by lifting to infinite-dimensional observable space: ``` State space (nonlinear) Observable space (linear) x_{t+1} = f(x_t) → (Kg)(x) = g(f(x)) ``` **Key property**: K is **linear** even when f is nonlinear. ## Connection to DMD DMD finds finite-rank approximation of K: ``` K ≈ Φ Λ Φ† ``` - Φ = DMD modes (approximate Koopman eigenfunctions) - Λ = eigenvalues ## As ACSet Morphism Koopman = natural transformation on observable presheaves: ```julia # Observable functor F: StateSpace → ObservableSpace # Koopman as pushforward K = f_*: Sh(X) → Sh(X) ``` ## GF(3) Triads ``` dmd-spectral (-1) ⊗ structured-decomp (0) ⊗ koopman-generator (+1) = 0 ✓ temporal-coalgebra (-1) ⊗ acsets (0) ⊗ koopman-generator (+1) = 0 ✓ ``` ## References - Brunton et al. "Modern Koopman Theory" (2021) - Mezić "Spectral Properties of Dynamical Systems" (2005) - PyDMD: https://github.com/mathLab/PyDMD
- Core Idea
- Connection to DMD
- As ACSet Morphism
- GF(3) Triads
- References
What does the koopman-generator skill do?
Koopman operator theory for infinite-dimensional linear lifting of nonlinear dynamics. Generates dynamics from observables.
How do I install it?
Run `npx skills add majiayu000/claude-skill-registry --skill koopman-generator --agent claude-code` — it drops the skill into your project so the agent can pick it up. Swap the --agent value for codex, cursor or copilot if you use one of those.
Where does this skill come from?
From majiayu000/claude-skill-registry, a repository with 534 stars. We read it straight from the repository tree rather than a submitted listing, so what you see here is what is actually published.
Is a popular skill a good skill?
Not necessarily. Stars measure attention, not adoption — a repository can trend for a week and be abandoned. That is why we show the weekly change from our own snapshots next to the total, instead of a single flattering number.