  A random forest regression based supervised machine learning method to
predict experimental critical temperature of superconductivity from the
electronic band structure, as obtained from Density Functional Theory, is
demonstrated. This complementarity between experiment and theory draws
inspiration from the merging of Kohn-Sham and Bogoliubov-De Gennes equations
[W. Kohn, W, EKU Gross, and LN Oliveira, Int. J. of Quant. Chem., 36(23),
611-615 (1989)]. Features in the Kohn-Sham Density Functional Theory band
structure away from EF becoming decisive for the superconducting gap
demonstrates this divide-and-conquer physical understanding. Not committing to
any microscopic mechanism for the SC at this stage, it implies that in
different classes of materials, different electronic features are responsible
for the superconductivity. However, training on known members of a class, the
performance of new members may be predicted. The method is validated for the
A15 materials, including both binary A3X and ternary A6XY intermetallics, A=V,
Nb, demonstrating that the two do indeed belong to the same class of
superconductors.
