  We present algorithms for performing data-driven stochastic reachability as
an addition to SReachTools, an open-source stochastic reachability toolbox. Our
method leverages a class of machine learning techniques known as kernel
embeddings of distributions to approximate the safety probabilities for a wide
variety of stochastic reachability problems. By representing the probability
distributions of the system state as elements in a reproducing kernel Hilbert
space, we can learn the "best fit" distribution via a simple regularized
least-squares problem, and then compute the stochastic reachability safety
probabilities as simple linear operations. This technique admits finite sample
bounds and has known convergence in probability. We implement these methods as
part of SReachTools, and demonstrate their use on a double integrator system,
on a million-dimensional repeated planar quadrotor system, and a cart-pole
system with a black-box neural network controller.
