NeuralLyapunov.jl
NeuralLyapunov.jl is a library for searching for neural Lyapunov functions in Julia.
This package provides an API for setting up the search for a neural Lyapunov function. Such a search can be formulated as a partial differential inequality, and this library generates a ModelingToolkit.jl PDESystem to be solved using NeuralPDE.jl. Since the Lyapunov conditions can be formulated in several different ways and a neural Lyapunov function can be set up in many different forms, this library presents an extensible interface for users to choose how they wish to set up the search, with useful pre-built options for common setups.
Getting Started
If this is your first time using the library, start by familiarizing yourself with the components of a neural Lyapunov problem in NeuralLyapunov.jl. Then, you can dive in with any of the following demonstrations (the damped simple harmonic oscillator is recommended to begin):
- Damped Simple Harmonic Oscillator
- Estimating the Region of Attraction
- Policy Search on the Driven Inverted Pendulum
- Benchmarking a neural Lyapunov method
When you begin to write your own neural Lyapunov code, especially if you hope to define your own neural Lyapunov formulation, you may find any of the following manual pages useful:
- Components of a Neural Lyapunov Problem
- Solving a Neural Lyapunov Problem
- Lyapunov Minimization Condition
- Lyapunov Decrease Condition
- Structuring a Neural Lyapunov function
- Training for Region of Attraction Identification
- Policy Search and Network-Dependent Dynamics
- Local Lyapunov analysis
Finally, when you wish to test your neural Lyapunov code, you may wish to use one of the built-in example systems: