Ab initio is a term that describes the scientific ‘lens’ used to describe and predic natural phenomena and behavior based on fundamental, first principles of physics. in latin “Ab Initio” literally means “from the beginning.” So,an ab initio simulation or calculation begins with the basic laws of quantum mechanics, without the application of any prior assumptions.
Classical electromagnetism theorizes the behavior of electrically charged particles and electric fields using first principles such as Faraday’s and Coulomb’s laws.
In this sense we do not think of Classical electromagnetism as an ab initio theory because it predicts the behavior of macroscopic fields, while computational material physics considers interactions on the atomic level.
Perhaps this is why many simulations using DFT are both time and relativity independent?