The simulation of complex systems affects many industrial and research fields and is important to verify the future behavior of a system. For hybrid systems [9], the heterogeneity of the discrete and continuous parts makes the modeling and simulation more difficult. Usually, numerical methods are chosen to simulate the continuous part of the models. However, their cost can be high when precision is needed and when interactions with the discrete part force rollbacks in the simulation. Other techniques are proposed to deal with uncertainties and expensive models, such as the flow-pipe methods [2] or qualitative modeling [8]. In this article, we present preliminary work to rely on a qualitative analysis of the model to supervise its simulation. Our goal is to build a qualitative map of the state space of the model in order to adapt the quantification of values and the discretization of time of the integration method. We expect this supervisor to optimize the time/precision balance, especially in the case of complex systems with many components.