My interpretation is that all mathematical models start from some kind of assumption:
Classical mechanics -> Newtons laws
Quantum mechanics -> Schrodinger equation / Path integral formalism
Electromagnetism -> Coulomb law
Ab initio means that we are trying to predict the behavior of a system by making as little assumptions as possible, and avoiding phenomenological descriptions or experimental data. In that sense, I would only call quantum mechanics an ab initio model as it makes the least assumptions.