How does it integrate with category theory?

The skill treats the Koopman operator as a natural transformation on observable presheaves and an ACSet morphism, allowing for rigorous compositional modeling.

What is the primary purpose of the Koopman Generator?

The Koopman Generator is designed to linearize nonlinear dynamical systems by lifting them into an infinite-dimensional space of observables, making complex systems easier to analyze and predict.

Is this skill suitable for bioinformatics?

Yes, it includes scientific skill interleaving with Biopython and SciPy, making it applicable to biological sequence dynamics and complex bio-system modeling.

Does this skill support Dynamic Mode Decomposition (DMD)?

Yes, it provides the mathematical framework to find finite-rank approximations of the Koopman operator, which is the core principle behind DMD.

Koopman Generator

Name: Koopman Generator
Author: plurigrid

byplurigrid

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Data Science & ML

Linearizes nonlinear dynamical systems using Koopman operator theory to generate predictive models from observable data.

About

The Koopman Generator skill empowers Claude to apply Koopman operator theory for the analysis and prediction of complex nonlinear dynamics. By lifting state-space variables into an infinite-dimensional observable space, the skill transforms nonlinear problems into linear ones, facilitating advanced tasks such as Dynamic Mode Decomposition (DMD) and spectral analysis. This skill is ideal for researchers and engineers working in fluid dynamics, bioinformatics, and control systems who require structured, interpretable models derived from high-dimensional time-series data using category-theoretic frameworks like ACSets and GF(3) naturality.

Key Features

Lifts nonlinear dynamics to infinite-dimensional linear observable space
Ensures compositional coherence via GF(3) triad naturality
Implements ACSet morphisms for compositional dynamical modeling
2 GitHub stars
Performs Dynamic Mode Decomposition (DMD) for spectral approximation
Integrates with SciPy and Biopython for scientific computing workflows

Use Cases

Analyzing spectral properties of biological and physical dynamical systems
Extracting linear predictive models from complex nonlinear time-series data
Developing category-theoretic 'chemputer' models for topological analysis

About

Key Features

Lifts nonlinear dynamics to infinite-dimensional linear observable space
Ensures compositional coherence via GF(3) triad naturality
Implements ACSet morphisms for compositional dynamical modeling
2 GitHub stars
Performs Dynamic Mode Decomposition (DMD) for spectral approximation
Integrates with SciPy and Biopython for scientific computing workflows

Use Cases

Analyzing spectral properties of biological and physical dynamical systems
Extracting linear predictive models from complex nonlinear time-series data
Developing category-theoretic 'chemputer' models for topological analysis