  Sub-terahertz (subTHz) antennas will play an important role in the next
generations of wireless communication systems. However, when comes to the
subTHz frequency spectrum, the antenna fabrication tolerance needs to be
accurately considered during the design stage. The classic approach to studying
the average performance of an antenna design considering fabrication tolerances
is through the use of the Monte-Carlo (MC) method. In this paper, we propose an
adaptive polynomial chaos expansion (PCE) method for the uncertainty
quantification analysis of subTHz horn antennas with flat-top radiation
patterns. The proposed method builds a surrogate model of the antenna's
response to electromagnetic (EM) excitation and estimates its statistical
moments with accuracy close to the reference MC method, but with a much smaller
computational complexity of roughly two orders of magnitude. Moreover, the
surrogate model based on PCE can substitute full-wave EM solvers in producing
samples for electromagnetic quantities of interest, resulting in significant
computational efficiency gains during optimization tasks. To this end, we
successfully combined PCE with the particle swarm optimization method to design
the free parameters of a horn antenna at $95$ GHz for a flat-top gain.
