I primarily think of Ab Initio theories as contrasted with empirical theories. A simple metric is the number of parameters a theory takes. If a theory takes a heavy tome of parameters which are valid within certain conditions to predict something under said conditions then I consider that empirical. Such a theory is of course limited in its predictive capability. An ab-initio theory should seek to derive the empirically observed laws, and once having done so, attempt to conjecture as yet unobserved phenomena. If experiment contradicts the prediction then of course the theory is wrong. Of course if it is ‘correct’ this means only that it is a close approximation to the truth which can be further improved, i.e. classical celestial mechanics versus general relativity.
For example, whereas originally the ideal gas law was determined empirically, through statistical mechanics you can play around with hyper-spheres in phase space and derive the law analytically.Further corrections can be obtained through the virial expansion.
Under these criteria all of the above theories are ab-inito, as they all have predictive capability.