Quantum mechanics is a theory that aggregates a set of irreducible laws that can accurately predict experimental results and therefore is considered a ab initio model. The same way, classical mechanics can accurately predict the observed behavior of macroscopic phenomena, and therefore is considered a ab initio model. Electromagnetism, however, cannot satisfactory explain all the electromagnetic observable phenomena (the ultraviolet catastrophe, photoelectric effect, Compton scattering, stability of the atom, etc.). This “problems” in the models gave origin to the investigation of more fundamental underlying laws and electromagnetism was showed to be the special case of a set of more fundamental theories. Therefore, electromagnetism is not a ab initio model.
I disagree that an ab initio theory that fails in its predictions is not therefore ab initio: it simply is an insufficiently accurate theory. For example density functional theory predicts certain properties of certain solids incorrectly, but that does not make it empirical or non-ab-initio in any way.