A deformable mirror (DM) can be used as a dynamically variable wavefront corrector in optical paths for robotic vision and surveillance cameras because its surface shape can be changed and controlled by an array of actuators. Here, we demonstrate that a practically usable model for DM control can be achieved by optimizing regression models. We develop a calculation approach based on the influence function (IF) matrix, in which an actual DM model is introduced along with the uncertainties of surface control errors to generate simulation data. Then, the sampled simulation surface data are trained and the influence function is updated, thereby constructing the required surface profiles directly from an acquired model without the need for a sequence of measurements to obtain compensating data. In particular, an actual piezoelectric DM is applied as an example to demonstrate the calculation process. With consideration of the partial shape convergence, surfaces with a small minimum residual are achieved without the use of in situ measured data in various actuating signal solvers for general DM control, because little care is needed to simulate the variance convergence process when generating the compensating data. In particular, the method is useful for open-loop-control imaging applications.