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I think the Ab initio characteristic of a mathematical model mainly depends on the question/problem we want to find an answer to. Usually almost every model implies that we choose a limit to our abstraction: this means that for example when we talk about continuum mechanics (included in classical mechanics) we neglect the molecular structure of the matter, or another example can be the chemical reactions, that are just a representation of matter structure changes without taking into account the quantum effects and laws from which those structure are depending. The same can be said also for the electromagnetism, that can be considered based on the Maxwell equations and as an Ab initio model for macroscopic electromagnetic phenomena, but not in the case we consider quantum phenomena as the origins of the Maxwell equations.
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