ReddRadar
Agent skill
koopman-generator
Koopman operator theory for infinite-dimensional linear lifting of nonlinear dynamics. Generates dynamics from observables.
Install this agent skill to your Project
npx add-skill https://github.com/majiayu000/claude-skill-registry/tree/main/skills/data/koopman-generator
SKILL.md
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:
# 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
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