HEAs have witnessed an exponential rise in interest over the last decade and have attracted significant attention due to their potential for achieving unique properties. While on one hand the Edisonian approach that opens infinite possibilities of combining various elements to synthesize HEAs is time-consuming, on the other hand, the experimental recipes may not necessarily lead to specific solid-solution phases required for the strengthening mechanisms. Thus, an inverse design strategy is required to address this challenge. We develop a machine learning tool, trained to correlate structural metrics with alloy properties, to identify designer compositions with targeted mechanical properties and crystallographic phases from refractory multi-principal elements. In particular, we employ an artificial neural network scheme and engineer the dataset with the Hume-Rothery rules, lattice features and physical properties. The model predictions for the phases and Young’s moduli for equiatomic alloys composed of Mo-Ta-Ti-W-Zr elements show reasonable agreement with experimental measurements.