  Reachability analysis is at the core of many applications, from neural
network verification, to safe trajectory planning of uncertain systems.
However, this problem is notoriously challenging, and current approaches tend
to be either too restrictive, too slow, too conservative, or approximate and
therefore lack guarantees. In this paper, we propose a simple yet effective
sampling-based approach to perform reachability analysis for arbitrary
dynamical systems. Our key novel idea consists of using random set theory to
give a rigorous interpretation of our method, and prove that it returns sets
which are guaranteed to converge to the convex hull of the true reachable sets.
Additionally, we leverage recent work on robust deep learning and propose a new
adversarial sampling approach to robustify our algorithm and accelerate its
convergence. We demonstrate that our method is faster and less conservative
than prior work, present results for approximate reachability analysis of
neural networks and robust trajectory optimization of high-dimensional
uncertain nonlinear systems, and discuss future applications.
