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Surface quality is one of the most important indicators of the quality of machined parts. The analytical method of defining the arithmetic mean roughness is not applied in practice due to its complexity and empirical models are applied only for certain values of machining parameters. This paper presents the design and development of artificial neural networks (ANNs) for the prediction of the arithmetic mean roughness, which is one of the most common surface roughness parameters. The dataset used for ANN development were obtained experimentally by machining AA7075 aluminum alloy under various machining conditions. With four factors, each having three levels, the full factorial design considers a total of 81 experiments that have to be carried out. Using input factor-level settings and adopting the Taguchi method, the experiments were reduced from 81 runs to 27 runs through an orthogonal design. In this study we aimed to check how reliable the results of artificial neural networks were when obtained based on a small input-output dataset, as in the case of applying the Taguchi methodology of planning a four-factor and three-level experiment, in which 27 trials were conducted. Furthermore, this paper considers the optimization of machining parameters for minimizing surface roughness in machining AA7075 aluminum alloy. The results show that ANNs can be successfully trained with small data and used to predict the arithmetic mean roughness. The best results were achieved by backpropagation multilayer feedforward neural networks using the BR algorithm for training. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.