The optimization of a controlled process in a simulation without access to the model itself is a common scenario and very relevant to many chemical engineering applications. A general approach is to apply a black-box optimization algorithm to a parameterized control scheme. The success then depends on the quality of the parametrization that should be low-dimensional though rich enough to express the salient features. This work proposes using solution snapshots to extract dominant modes of the temporal dynamics of a process and use them for low-dimensional parametrizations of control functions. We provide theoretical reasoning and illustrate the performance for the optimal control of a methanation reactor.