KantorovichAbstraction.jl

This repository contains all the code necessary to implement the experiments in

• [BRAJ23] Adrien Banse, Licio Romao, Alessandro Abate, Raphaël M. Jungers - Data-driven abstractions via adaptive refinements and a Kantorovich metric - Online here

[BRAJ23, Fig. 3.] Illustration of the execution of [BRAJ23, Algorithm 2].

Content

src/Kantorovich.jl module is composed of the following files:

• src/metric.jl - contains an efficient implementation of the Kantorovich metric [BRAJ23, Algorithm 1], as well as structures for Markov chains
• src/abstraction.jl - contains an implementation of [BRAJ23, Algorithm 2]
• src/system.jl - contains structures for dynamical systems
• src/utils.jl - contains util functions

And experiments/refine_memory_example.ipynb is a notebook implementing [BRAJ23, Section III-C], and recovers all the numerical values exposed in this section.

[BRAJ23, Fig. 5.] Illustration of the last partitioning given by [BRAJ23, Algorithm 2] for [BRAJ23, Example 1].