I think quantum physics is called an ab-initio model because it fits the definition given above. It describes the behaviour and properties of small scale particles by means of fundamental properties of them which you can not further reduce to other ones.
The same goes for classical mechanics. Starting from a few very simple equations and terms, you can describe a whole range of interactions and properties of objects. But these starting points can not be replaced by ones which are more fundamental.
As for classical electromagnetism, I don’t think it is. I would think it can be reduced further.
I would like to revise my answer about classical electromagnetism, as after reading a coupe of other posts I do believe it is an ab-initio model starting from Maxwell’s equations. As for the other questions I think I now have a better understanding of them as when I posted before