  The deployment of autonomous systems that operate in unstructured
environments necessitates algorithms to verify their safety. This can be
challenging due to, e.g., black-box components in the control software, or
undermodelled dynamics that prevent model-based verification. We present a
novel verification framework for an unknown dynamical system from a given set
of noisy observations of the dynamics. Using Gaussian processes trained on this
data set, the framework abstracts the system as an uncertain Markov process
with discrete states defined over the safe set. The transition bounds of the
abstraction are derived from the probabilistic error bounds between the
regression and underlying system. An existing approach for verifying safety
properties over uncertain Markov processes then generates safety guarantees. We
demonstrate the versatility of the framework on several examples, including
switched and nonlinear systems.
