## 3 Materials and Methods
### Machine Learning in Support of Deformation Detection  
Machine learning algorithms can help solve specific tasks without being explicitly programmed, relying instead on patterns learned from a training dataset. We here show how trained Convolutional Neural Networks (CNN) can be plugged into the workflow to automatically detect large ground deformation in interferograms (Figure 4). Synthetic data was first generated to train the network. The goal was to produce synthetic interferograms, wrapped and orthorectified, depicting realistic deformation fringes and phase decorrelation related to various artifacts (i.e., atmospheric phase delays, geometric distortions due to orthorectification, phase decorrelation due to vegetated areas, etc.). We synthesized the data from a combination of procedural noise and empirical rules, which although not physically motivated, can express a wide range of patterns similar to those found in real data (at least locally). The network was designed as a fully convolutional auto encoder built out of residual learning blocks (inspired by ResNet, [73]). Details on the synthetic data generation and network architecture can be found in Supplementary Material S2, and the trained CNN can be accessed on a Github repository ([[https://github.com/[PERSON]/SAR-InterfPhaseFilter](https://github.com/[PERSON]/SAR-InterfPhaseFilter)]([https://github.com/[PERSON]/SAR-InterfPhaseFilter](https://github.com/[PERSON]/SAR-InterfPhaseFilter))). The network was then trained to recover from the synthetic interferograms (provided as input), the associated phase gradients and phase decorrelation mask (expected outputs), Figure 4a. Once trained, the network is plugged into the processing pipeline (Figure 4b): newly generated interferograms are fed through this pre-trained network, which yields both the phase gradients and phase decorrelation (i.e., noise mask). Unwrapping of these phase gradients is successively performed to recover approximate ground displacements (Figure 4c), where robustness against artifacts that might trigger false alarms is preferred over precise phase differences. The unwrapping simply solves for a displacement map whose gradients match the gradients estimated by the CNN. Since the CNN performs the filtering of the gradients and detection of noise, treatment of decorrellated areas in the unwrapping is rather simple. From this displacement map a deformation score is ultimately computed (DEF), as the standard deviation of the displacements expressed in meters in the radar line-of-sight (LOS). This data is then disseminated (Figure 4d) and can be used to plot time series that allow for identification of strong deformation events. In addition, automated email alerts are sent to interested users when a threshold is exceeded. Based on empiric evaluation of all 17 volcanoes currently monitored by MOUNTS, representing a total of >1360 interferograms, the threshold was set to 0.001 m. This value can however be tuned for each volcano, to adapt to specific volcanic activity or monitoring requirements. A similar approach involving CNN has been presented by [34] to detect large deformation signals in short-duration, wrapped and geocoded interferograms.