We consider the problem of safety assessment of a dynamical system for which no model and just limited data on the states is available. That is, given samples of the state {x(t_i)}^N_i=1 at time instances t₁ ≤ t₂ ≤ ··· ≤ t_N and some other side information in terms of the regularity of the state evolutions, we are interested in checking whether x(T) ∉ Xu, where T > t_N and Xu ⊂ Rⁿ (the unsafe set) are pre-specified. To this end, we use piecewise-polynomial approximations of the trajectories based on the data along with the regularity side information to formulate a data-driven differential inclusion model. For these classes of data-driven differential inclusions, we propose a safety assessment theorem based on barrier certificates. The barrier certificates are then found using polynomial optimization. The method is illustrated by two examples.