The occurrence of instabilities in chemically reacting systems, resulting in unsteady and spatially inhomogeneous reaction rates, is a widespread phenomenon. In this article, we use nonlinear signal processing techniques to extract a simple, but accurate, dynamic model from experimental data of a system with spatiotemporal variations. The approach consists of a combination of two steps. The proper orthogonal decomposition [POD or Karhunen-Loeve (KL) expansion] allows us to determine active degrees of freedom (important spatial structures) of the system. Projection onto these ''modes'' reduces the data to a small number of time series. Processing these time series through an artificial neural network (ANN) results in a low-dimensional, nonlinear dynamic model with almost quantitative predictive capabilities. This approach is demonstrated using spatiotemporal data from CO oxidation on a Pt (110) crystal surface. In this special case, the dynamics of the two-dimensional reaction profile can be successfully described by four modes, the ANN-based model not only correctly predicts the spatiotemporal short-term behavior, but also accurately captures the long-term dynamics (the attractor). While this approach does not substitute for fundamental modeling, it provides a systematic framework for processing experimental data from a wide variety of spatiotemporally varying reaction engineering processes.