What I understood from this page is that if we are able to present a mathematical model based upon a set of principals or mathematical laws which can well explain the natural phenomenon and is also able to predict (given the initial condition) the time evolution of a system, then such a model can be called an ab initio model. On this premise classical and quantum mechanics are catagorised as ab initio models. Because given the Newton’s Laws ( Which govern both the rotational (?) and linear dynamics ) and initial conditions we can predict and explain motion of classical objects very well. Similarly for Quantum mechanics the probabilistic predictions have been found to be correct and natural phenomenon like atomic spectrum have been explained well. For classical electromagnetism Maxwells equations might be considered as the first principals but some very fundamental questions like why the continuity equation which governs the refraction and reflection has to be the way it is, is not clear to me.