  We present a data-driven method for computing approximate forward reachable
sets using separating kernels in a reproducing kernel Hilbert space. We frame
the problem as a support estimation problem, and learn a classifier of the
support as an element in a reproducing kernel Hilbert space using a data-driven
approach. Kernel methods provide a computationally efficient representation for
the classifier that is the solution to a regularized least squares problem. The
solution converges almost surely as the sample size increases, and admits known
finite sample bounds. This approach is applicable to stochastic systems with
arbitrary disturbances and neural network verification problems by treating the
network as a dynamical system, or by considering neural network controllers as
part of a closed-loop system. We present our technique on several examples,
including a spacecraft rendezvous and docking problem, and two nonlinear system
benchmarks with neural network controllers.
