This paper proposes the use of an artificial neural network (ANN) for solving one of the ongoing research challenges in finite set-model predictive control (FS-MPC) of power electronics converters, i.e., the automated selection of weighting factors in cost function. The first step in this approach is to simulate a detailed converter circuit model or run experiments numerous times using different weighting factor combinations. The key performance metrics e.g., average switching frequency (<inline-formula><tex-math notation="LaTeX">f_{{\rm sw}}</tex-math></inline-formula>) of the converter, total harmonic distortion, etc. are extracted from each simulation. This data is then used to train the ANN, which serves as a surrogate model of the converter that can provide fast and accurate estimates of the performance metrics for any weighting factor combination. Consequently, any arbitrary user-defined fitness function that combines the output metrics can be defined and the weighting factor combinations that optimize the given function can be explicitly found. The proposed methodology was verified on a practical weighting factor design problem in FS-MPC regulated voltage source converter for uninterruptible power supply system. Designed weighting factors for two exemplary fitness functions turned out to be robust to load variations and to yield close to expected performance when applied both to detailed simulation model (less than 3% error) and to experimental test bed (less than 10% error).