Support vector machines for learning reactive islands
This work addresses the challenge of quantifying transition dynamics in dynamical systems for researchers in physics and applied mathematics, but it is incremental as it adapts an existing machine learning method to a specific domain.
The authors tackled the problem of learning reactive islands in Hamiltonian systems by developing a support vector machine framework that directly identifies these phase space structures without first computing unstable periodic orbits and their manifolds, applied to the Hénon-Heiles benchmark system.
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 Hénon-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.