The development of phonocardiography processing methods is gradually becoming more important as the amount of data increases due to the ease and low cost of such measurements. To improve diagnosis and aid medical experts, heart sound-based disorder classification methods have been introduced. However, most of these methods rely on an accurately segmented phonocardiogram signal. This can be achieved in a multitude of ways, the most widely used being the hidden semi-Markov model with logistic regression. However, with the introduction of large, labeled databases, such as the PhysioNet challenge databases, artificial neural network-based segmentation became a possibility. We used a U-net-based convolutional neural network architecture to segment fetal heart sounds from abdominal recordings. The model was trained on an open pediatric dataset and then later finetuned for fetal data. We compared the performance of this model to the results of our previously developed hidden semi-Markov model method on this data, as well as the original hidden semi-Markov model with logistic regression. Our experiments showed a 92.2% PPV, 84.9% F1 and 17.2±26.0 ms mean absolute error for the first, and 88.1% PPV, 88.1% F1 and 17.9±12.7 mean absolute error for the second heart sound detection for the best neural network model. We found that while neural network first heart sound detection could not reliably outperform the other tested methods, the second heart sound detection accuracy improved. This opens a possibility that with a specifically trained neural network and hidden semi-Markov temporal modeling a more accurate method can be achieved.