  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.
