One of the many challenges proposed by the ongoing COVID-19 pandemic is to explain the spread of the disease through suitable equations and capture the epidemic’s features through the parameters of the mathematical model. However some of these values cannot be pre-determined nor measured precisely, hence other estimation procedures are needed. Machine Learning has been extensively used as a parametric and data-based model identification technique. In this project we use Machine Learning with the purpose of testing and exploiting the learning capability of Artificial Neural Networks (in particula, Feed Forward Neural Networks), applied to noisy, real-world data, to obtain a better estimation of the unknown parameters of epidemiological compartmental models. Motivated by the effectiveness of Machine Learning, we used the trained neural network to estimate the basic reproduction number of the COVID-19 epidemic and the contagion rate of the disease. We conclude that a neural-network-informed calibration method provides a reliable result, when compared with standard techniques.