How does this skill relate to Dynamic Mode Decomposition (DMD)?

This skill utilizes DMD to find finite-rank approximations of the Koopman operator, providing practical numerical methods for spectral decomposition of data.

What is the Koopman operator used for?

The Koopman operator is used to represent non-linear dynamical systems as linear systems in a higher-dimensional space of observables, which simplifies complex system analysis and prediction.

Can this skill be used for bioinformatics research?

Yes, it is designed to interleave with scientific ecosystems like biopython and bicomodule to analyze biological sequences and complex chemical dynamics.

What mathematical frameworks does this skill support?

It supports category theory applications (Cat#), ACSet morphisms, and GF(3) triads to ensure mathematical consistency in complex system modeling.

Is the Koopman Generator compatible with standard Python libraries?

Yes, it specifically integrates with Scipy and other scientific computing libraries to perform numerical lifting and generator structures.

Koopman Dynamics Generator

Name: Koopman Dynamics Generator
Author: plurigrid

byplurigrid

•

Data Science & ML

Linearizes non-linear dynamical systems using Koopman operator theory to generate predictive models from observables.

The Koopman Generator skill empowers Claude to apply advanced Koopman operator theory for modeling complex, non-linear dynamical systems. By lifting state-space data into infinite-dimensional observable spaces, it transforms non-linear problems into linear ones, facilitating easier analysis, spectral decomposition, and prediction. This skill integrates sophisticated mathematical concepts including Dynamic Mode Decomposition (DMD) and ACSet morphisms, making it an essential tool for researchers and engineers working in scientific computing, bioinformatics, and topological systems theory.

Key Features

01Linearizes non-linear dynamics through infinite-dimensional observable lifting

02Integrates with Scipy for high-performance numerical scientific computing

03Implements finite-rank approximations via Dynamic Mode Decomposition (DMD)

04Ensures compositional coherence via GF(3) naturality and triad interleaving

05Provides category-theoretic modeling using ACSet morphisms and functors

068 GitHub stars

Use Cases

01Developing linear controllers for inherently non-linear physical processes

02Predicting complex system behavior in fluid dynamics or bioinformatics

03Analyzing high-dimensional time-series data using spectral decomposition

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi koopman-generator

For use in Claude.ai and ChatGPT

Download Skill