Industrial applications of conductive polymer composites with carbon nanotubes require precise tailoring of their electrical properties. While existing theoretical methods to predict the bulk conductivity require fitting to experiments and often employ power-laws valid only in the vicinity of the percolation threshold, the accuracy of numerical methods is accompanied with substantial computational efforts. In this paper we use recently developed physically-based finite element analyses to successfully train an artificial neural network to make predictions of the bulk conductivity of carbon nanotube-polymer composites at negligible computational cost.