In this subsection we study how the TD-ADGA algorithm fares when it must determine a more difficult potential energy surface. To do this we will investigate how well the TD-ADGA method describe a double-well potential that is discovered during a dynamics simulation. To do this, the time-dependent wave function is initialized from a VSCF state localized in one well of a double-well potential and only during the time-propagation will the wave function reach the other well of the system. The TD-ADGA algorithm must thus be able to detect that the wave function is located in a double-well potential and fit a potential energy surface effectively for the dynamics to be accurate.