koopman-generator
Koopman operator theory for infinite-dimensional linear lifting of nonlinear dynamics. Generates dynamics from observables.
Best use case
koopman-generator is best used when you need a repeatable AI agent workflow instead of a one-off prompt.
Koopman operator theory for infinite-dimensional linear lifting of nonlinear dynamics. Generates dynamics from observables.
Teams using koopman-generator should expect a more consistent output, faster repeated execution, less prompt rewriting.
When to use this skill
- You want a reusable workflow that can be run more than once with consistent structure.
When not to use this skill
- You only need a quick one-off answer and do not need a reusable workflow.
- You cannot install or maintain the underlying files, dependencies, or repository context.
Installation
Claude Code / Cursor / Codex
Manual Installation
- Download SKILL.md from GitHub
- Place it in
.claude/skills/koopman-generator/SKILL.mdinside your project - Restart your AI agent — it will auto-discover the skill
How koopman-generator Compares
| Feature / Agent | koopman-generator | Standard Approach |
|---|---|---|
| Platform Support | Not specified | Limited / Varies |
| Context Awareness | High | Baseline |
| Installation Complexity | Unknown | N/A |
Frequently Asked Questions
What does this skill do?
Koopman operator theory for infinite-dimensional linear lifting of nonlinear dynamics. Generates dynamics from observables.
Where can I find the source code?
You can find the source code on GitHub using the link provided at the top of the page.
SKILL.md Source
# 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/PyDMDRelated Skills
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