  We build random forests models to predict elastic properties and mechanical
hardness of a compound, using only its chemical formula as input. The model
training uses over 10,000 target compounds and 60 features based on
stoichiometric attributes, elemental properties, orbital occupations, and ionic
bonding levels. Using the models, we construct triangular graphs for B-C-N
compounds to map out their bulk and shear moduli, as well as hardness values.
The graphs indicate that a 1:1 B-N ratio can lead to various superhard
compositions. We also validate the machine learning results by evolutionary
structure prediction and density functional theory. Our study shows that
BC$_{10}$N, B$_4$C$_5$N$_3$, and B$_2$C$_3$N exhibit dynamically stable phases
with hardness values $>40$GPa, which are potentially new superhard materials
that could be synthesized by low-temperature plasma methods.
