Accurate determination of total fusion and fusion-evaporation reaction cross-sections is an important task in experimental nuclear physics studies. In this study, we estimated the total fusion cross-sections and, as an example, one of the particular channels (2n) cross-sections for different reactions by using artificial neural network (ANN) methods. The root mean square errors for fusion reaction were obtained as 18.5 and 110.4 mb for the training and test data, which correspond to 1.8% and 10.5% deviations from the experimental cross-section values, respectively. These values for the 2n channel are 0.3% for training and 13.3% for test data of ANN. The deviations are mostly lower than the cross-section values from a commonly used theoretical calculation code. The results indicate that ANN methods might be a possible candidate tool for the estimation of cross-sections for fusion and fusion-evaporation reactions.