We present a numerical method for solving the unsteady Boltzmann equation describing rarefied gas dynamics flows based on the combination of a wieghted particle approach on a Cartesian lattice and a fast spectral schemes for the collisional integral. We will also discuss the extension of such method to the case of electromagnetic conducting fluids and how to take into account the quantification of uncertainty in these models. Several numerical tests will explore the capability of the scheme proposed in modeling transport phenomena.