In the TD-ADGA developed in the present work, the main idea is to grow the PES according to the needs of a wavefunction evolving in time. This means that the PES obtained using the TD-ADGA method must be updated during the dynamics simulation to ensure similar accuracy at all times. We use similar convergence criteria as in the original TI-ADGA method but generalized and augmented with new convergence conditions tailored the time-dependent context. To generalize the TI-ADGA to the time-dependent case, a time-dependent wave function density is used in order to obtain the ADGA integrals involved in identifying needed SPs. We thus define the reduced one-mode densities for a general time-dependent nuclear wave function. We then use densities obtained with the time-dependent Hartree (TDH) and multi configuration time-dependent Hartree (MCTDH) wave functions. The TD-ADGA procedure can in general be used with any time-dependent wave function method as long as a wave function density can be formulated. In future woork, we expect to combine the methods with time-dependent vibrational coupled cluster methods. In this work we exclusively consider single surface computations. The wave function may be initiated from a wave function obtained on another surface but the simulated time-dependent dynamics and PES construction is restricted to a single surface. Extension to multiple adiabatic or diabatic surfaces and non-adiabatic events are anticipated to be possible along similar lines but require significant extensions and are subjects of future research.