Simulating the dynamics of molecular systems is key to understanding many processes of nature, as such simulations can give insights into the fundamental molecular motions and chemical reactions involved. Full quantum mechanical simulations of molecules have the promise of accurately revealing molecular dynamics from first principles, but high computational costs and complex workflows often make such computations prohibitive to apply in practice. There are two major challenges inherent to any quantum molecular dynamics computation i) how to represent and compute the potential energy surface (PES) that the dynamics takes place on and ii) how to represent and propagate accurate in time, the wave function for nuclear motion on the PES. These two problems are tightly connected as on one hand, the PES dictates how the wave function for nuclear motion evolves over time while on the other hand, it is difficult to know quantitatively which domains of the PES the wave function visits before carrying out an accurate dynamics simulation. Two opposite strategies have been prevailing for dealing with the PES issue in time-dependent simulations.