Quantum physics and classical mechanics are both ab initio models since they rely on a set of mathematical propositions that govern the behaviour of the system, and we then test the resulting emergent behaviour of these systems against reality through experiments.
Classical electromagnetism proposes a set of equations that govern electromagnetic fields, but these aren’t emergent from more fundamental principles (at least in classical electromagnetism).
I guess my question would be “how far down” does it have to be to be ab initio? Even the Schrodinger equation might be described as an emergent effect of a more fundamental process.
I suppose the distinction might be that ab initio describes an idea that leads to emergent behaviour that describes reality, as opposed to specific sets of equations developed to be “fit” to what we see in reality.