In the following subsections, we will describe the theoretical background for the TD-ADGA. First, we will set up some preliminaries on the form of the PES representation and on the description of the time-dependent wave functions for nuclear motion and their reduced one-mode densities. We will then describe the time-independent ADGA method and generalize this to the time-dependent ADGA method, including how automatic decisions for PES updates are made and different options for updating the dynamics with an updated PES.