The construction of reduced order models for dynamical systems usingproper orthogonal decomposition (POD) is based on the informationcontained in so-called snapshots. These provide the spatialdistribution of the dynamical system at discrete time instances.This work is devoted to optimizing the choice of these timeinstances in such a manner that the error between the POD-solutionand the trajectory of the dynamical system is minimized. First andsecond order optimality systems are given. Numerical examplesillustrate that the proposed criterion is sensitive with respect tothe choice of the time instances and further they demonstrate thefeasibility of the method in determining optimal snapshot locationsfor concrete diffusion equations.
