What is meant by 'lifting' in this context?

Lifting refers to the process of mapping a low-dimensional nonlinear state space into a higher-dimensional space of functions (observables) where the evolution becomes linear.

Does this skill require specific mathematical libraries?

While the skill provides the theoretical framework and implementation patterns, it is ideally used alongside libraries like PyDMD or Julia's Catlab.jl for ACSet manipulations.

What is the primary function of the Koopman Generator?

It uses Koopman operator theory to linearize nonlinear dynamics by lifting the state space into an infinite-dimensional observable space, making complex systems easier to analyze.

Who should use the Koopman Generator skill?

It is designed for data scientists, physicists, and engineers working with complex dynamical systems, control theory, or advanced spectral analysis.

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

DMD provides a finite-rank approximation of the Koopman operator. This skill uses DMD modes and eigenvalues to represent the underlying dynamics of a system.

Koopman Generator

Name: Koopman Generator
Author: plurigrid

byplurigrid

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データサイエンスとML

Linearizes complex nonlinear dynamics using Koopman operator theory to enable predictive modeling through observable space.

概要

The Koopman Generator skill leverages Koopman operator theory to transform nonlinear dynamical systems into infinite-dimensional linear representations. By lifting state-space dynamics into observable space, it allows Claude to analyze, predict, and decompose complex behaviors using linear algebraic techniques like Dynamic Mode Decomposition (DMD). This skill is particularly useful for scientific computing, control theory, and advanced data analysis where traditional nonlinear modeling is computationally difficult, providing a rigorous mathematical framework based on ACSets and Category Theory for structural consistency.

主な機能

Observable presheaf mapping using ACSet morphisms
Spectral analysis of complex dynamical systems
Dynamic Mode Decomposition (DMD) spectral approximation
2 GitHub stars
Nonlinear-to-linear system transformation via lifting
Dynamics generation from experimental observables

ユースケース

Developing linear controllers for inherently nonlinear processes
Analyzing spectral properties of high-dimensional time-series data
Predicting the evolution of complex physical or chemical systems

概要

主な機能

Observable presheaf mapping using ACSet morphisms
Spectral analysis of complex dynamical systems
Dynamic Mode Decomposition (DMD) spectral approximation
2 GitHub stars
Nonlinear-to-linear system transformation via lifting
Dynamics generation from experimental observables

ユースケース

Developing linear controllers for inherently nonlinear processes
Analyzing spectral properties of high-dimensional time-series data
Predicting the evolution of complex physical or chemical systems