Support vector machines for learning reactive islands

TL;DR

This paper introduces a support vector machine-based method to identify reactive islands in phase space of Hamiltonian systems, enabling direct detection without computing unstable periodic orbits.

Contribution

The paper presents a novel SVM framework for learning reactive islands directly from trajectory data in Hamiltonian systems, bypassing the need for unstable periodic orbit computation.

Findings

Successfully applied to Hénon-Heiles system

Allows direct identification of reactive islands

Discusses sampling and learning strategies

Abstract

We develop a machine learning framework that can be applied to data sets derived from the trajectories of Hamilton's equations. The goal is to learn the phase space structures that play the governing role for phase space transport relevant to particular applications. Our focus is on learning reactive islands in two degrees-of-freedom Hamiltonian systems. Reactive islands are constructed from the stable and unstable manifolds of unstable periodic orbits and play the role of quantifying transition dynamics. We show that support vector machines (SVM) is an appropriate machine learning framework for this purpose as it provides an approach for finding the boundaries between qualitatively distinct dynamical behaviors, which is in the spirit of the phase space transport framework. We show how our method allows us to find reactive islands directly in the sense that we do not have to first compute unstable periodic orbits and their stable and unstable manifolds. We apply our approach to the H\'enon-Heiles Hamiltonian system, which is a benchmark system in the dynamical systems community. We discuss different sampling and learning approaches and their advantages and disadvantages.