Abstract: A process and an apparatus control the growth of a crystal, which growth is governed by a set of measurable and non-measurable variables. The process includes establishing an on-line simulation software working with a reduced number of variables, the reduction of variables being performed by using a projection algorithm; speeding up the on-line simulation software by generating data banks in which values of off-line precalculated variables are stored; tuning the on-line simulation software by adjusting the results predicted by on-line simulations to the results obtained by off-line simulations and by measurements; and establishing a control loop and controlling at least one of the variables in real time, the control loop using the speeded up and tuned on-line simulation software as an on-line observer.