Data-driven Identification of Attractors Using Machine Learning

TL;DR

This paper presents a machine learning approach to discretize phase space and identify attractors in dynamical systems, leveraging neural networks trained on orbit data to analyze global dynamics topologically.

Contribution

It introduces a novel neural network-based discretization method for phase space that aligns with Conley's topological framework to characterize attractors.

Findings

Effective discretization of phase space achieved

Neural network approximations reveal attracting neighborhoods

Framework aligns with topological dynamical systems theory

Abstract

In this paper we explore challenges in developing a topological framework in which machine learning can be used to robustly characterize global dynamics. Specifically, we focus on learning a useful discretization of the phase space of a flow on compact, hyperrectangle in $\mathbb{R}^n$ from a neural network trained on labeled orbit data. A characterization of the structure of the global dynamics is obtained from approximations of attracting neighborhoods provided by the phase space discretization. The perspective that motivates this work is based on Conley's topological approach to dynamics, which provides a means to evaluate the efficacy and efficiency of our approach.