  We present an algorithm for data-driven reachability analysis that estimates
finite-horizon forward reachable sets for general nonlinear systems using level
sets of a certain class of polynomials known as Christoffel functions. The
level sets of Christoffel functions are known empirically to provide good
approximations to the support of probability distributions: the algorithm uses
this property for reachability analysis by solving a probabilistic relaxation
of the reachable set computation problem. We also provide a guarantee that the
output of the algorithm is an accurate reachable set approximation in a
probabilistic sense, provided that a certain sample size is attained. We also
investigate three numerical examples to demonstrate the algorithm's
capabilities, such as providing non-convex reachable set approximations and
detecting holes in the reachable set.
