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Context. Filaments are ubiquitous in the Galaxy, and they host star formation. Detecting them in a reliable way is therefore key towards our understanding of the star formation process. Aims. We explore whether supervised machine learning can identify filamentary structures on the whole Galactic plane. Methods. We used two versions of UNet-based networks for image segmentation.We used H2 column density images of the Galactic plane obtained with Herschel Hi-GAL data as input data. We trained the UNet-based networks with skeletons (spine plus branches) of filaments that were extracted from these images, together with background and missing data masks that we produced. We tested eight training scenarios to determine the best scenario for our astrophysical purpose of classifying pixels as filaments. Results. The training of the UNets allows us to create a new image of the Galactic plane by segmentation in which pixels belonging to filamentary structures are identified. With this new method, we classify more pixels (more by a factor of 2 to 7, depending on the classification threshold used) as belonging to filaments than the spine plus branches structures we used as input. New structures are revealed, which are mainly low-contrast filaments that were not detected before.We use standard metrics to evaluate the performances of the different training scenarios. This allows us to demonstrate the robustness of the method and to determine an optimal threshold value that maximizes the recovery of the input labelled pixel classification. Conclusions. This proof-of-concept study shows that supervised machine learning can reveal filamentary structures that are present throughout the Galactic plane. The detection of these structures, including low-density and low-contrast structures that have never been seen before, offers important perspectives for the study of these filaments.