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The paper addresses practical capabilities of artificial neural networks (ANNs) in developing measurement-based continuous-time dynamic equivalents for power systems. Our method is based on a set of measurements at boundary nodes between a subsystem that is to be modeled in detail ("retained" portion of the system) and the part that is to be replaced by a simplified ("equivalent") model. We are particularly interested in combining standard physics-based models with signal-based models derived from measurements. We utilize a color-coding scheme to distinguish between physics-based models (clear or white box) at one end, the signal-based models (opaque or black box) at the opposite end, and mixed (gray box) models in the middle. The paper also proposes a way for combining classical and ANN-based equivalents in a hybrid model implemented in a standard software environment for transient analysis (in this case, ETMSP). Our conclusions are based on simulations performed on a model of a benchmark multimachine power system derived from the WSCC system.