## 5 Conclusions  
We introduced a new machine-learning approach to map recent lava flows that exploits the high spatial resolution and freely available information coming from Sentinel 2-MSI channels. Our approach relies on a k-medoids unsupervised classifier, able to separate the data points in \(n\) different clusters, depending on the correlation measure among the pixels belonging to the area of interest. Although this method allows to group pixels having similar trends, it is not able to properly discriminate pixels belonging to recent lava flow and pixels not belonging to it. Thus, a second step relying on a Bayesian neural network is performed to map recent lava flows. Three recent effusive eruptions at Mount Etna were investigated, namely February-April 2017, August 2018 and December 2018. The results show that the BNN outcomes are in good agreement with the target in all the three eruptions. It is worth noting that the reference lava flow maps that have been used to validate our approach have been manually produced by using PlanetScope data; these images are very detailed, but not freely available and quite expensive. Even though some isolated pixels are wrongly classified as belonging to the lava flow, our machine-learning approach is able to correctly identify the main lava flow body by only knowing at most 0.02% of the lava flow field. In fact, very few labelled pixels are sufficient to get a coarse lava flow map from the BNN, but the performance of this approach can further be improved by increasing the number of labelled pixels. Overall, our BNN classifier produces excellent results, especially when the available images are recorded within few weeks of the end of the lava emission; after this period of time, the performances get worse. Although the performance is largely improved by using more pixels per class, this would mean knowing a-priori more points belonging to the lava flow. Lava-flow maps produced adopting this approach can be used to facilitate field mapping, giving insights into emplacement processes, and improving the monitoring and assessment of lava flow hazards. It is noteworthy that by using this technique, only the geo-located and calibrated 10-m Sentinel 2-MSI images and a few labelled pixels are needed to map lava flows with 10 m spatial resolution. Furthermore, although MATLAB enables the use of GPUs to accelerate time-processing, most of the processing can be run on a common laptop with processing time varying from 2 min to 15 min, depending on the size of the lava flow, thus representing a valuable time-saving mapping tool. This method has been applied to Mount Etna, but our machine-learning approach has been designed to be applicable to other volcanic areas. Conceptualization, C.C. and G.G. ; Data curation, G.G. ; Funding acquisition, A.H. and C.D.N. ; Methodology, C.C. and G.B. ; Software, C.C. ; Supervision, C.D.N. ; Validation, A.C.; Writing--Original draft, C.C., G.G. and A.C.; Writing--Review & Editing, G.B. and C.D.N. This research was partially funded by the ATHOS Research Programme. This work was developed within the framework of the Laboratory of Technologies for Volcanology (TecnoLab) at INGV in Catania (Italy). Sentinel-2 images are courtesy of the Copernicus Open Access Hub ([[https://sciubub.copernicus.eu](https://sciubub.copernicus.eu)]([https://sciubub.copernicus.eu](https://sciubub.copernicus.eu))). Pleiades data were available through the Space Volcano Observatory with Pleiades (SVOP) project coordinated by [PERSON] ([[http://volcano.iterre.fr/svo_projects](http://volcano.iterre.fr/svo_projects)]([http://volcano.iterre.fr/svo_projects](http://volcano.iterre.fr/svo_projects))). We would like to thank Planet Labs, Inc. for providing the PlanetScope imagery through the Education and Research Program.