Monitoring vital signs of neonates can be harmful and lead to developmental troubles. Ballistocardiography, a contactless heart rate monitoring method, has the potential to reduce this monitoring pain. However, signal processing is uneasy due to noise, inherent physiological variability and artifacts (e.g. respiratory amplitude modulation and body position shifts). We propose a new heartbeat detection method using neural networks to learn this variability. A U-Net model takes thirty-second-long records as inputs and acts like a nonlinear filter. For each record, it outputs the samples probabilities of belonging to IJK segments. A heartbeat detection algorithm finally detects heartbeats from those segments, based on a distance criterion. The U-Net has been trained on 30 healthy subjects and tested on 10 healthy subjects, from 8 to 74 years old. Heartbeats have been detected with 92% precision and 80% recall, with possible optimization in the future to achieve better performance.