## 3 Materials and Methods
### Machine Learning in Support of Deformation Detection
The main differences to our approach are the following: (i) training is performed on real interferograms, combined with a data augmentation approach to increase the number of interferograms where deformation is recorded; we instead create synthetic training data, allowing the generation of an unlimited number of interferograms, and avoiding the time-consuming task of labeling interferograms where deformation is identified; (ii) edge detection is applied to the interferograms (during both training and prediction processes), to identify phase jumps between fringes, which are subsequently considered as noise-free regions where deformation can be detected; our network instead is trained to output a decorrelation mask informing on the degree of phase noise, successively used to filter noisy regions in the interferogram where erroneous gradients could be detected, (iii) the network output is a deformation probability; our network outputs clean phase gradients (and decorrelation mask for additional cleaning), which can be successively unwrapped to compute ground deformation maps, from which a physically meaningful score can be derived (i.e., standard deviation expressed in meters), (iv) the authors fine-tuned a popular network (AlexNet, [74]), whereas the architecture of our network was designed from scratch and trained on our synthetic dataset, thereby allowing more flexibility in the desired outputs. We compare the performances of the two approaches using the same evaluation metrics used in their study, which are derived from the confusion matrix: accuracy (ratio between correctly predicted samples and all testing samples), true positive rate (TPR, ratio between correctly identified positive samples and all positive samples), and true negative rate (TNR, ratio between correctly identified negative samples and all negative samples). Table 2 shows the performances of both networks, tested on the same volcanoes (Erta Ale, Ethiopia, and Etna, Italy), and highlights the good performances of our CNN. Figure 4: Workflow to detect ground deformation using a pre-trained convolutional network: (**a**) Convolutional Neural Network (CNN) training using synthetic data (see Supplementary Material S2), (**b**) operational usage of the pre-trained CNN to detect to detect phase gradients and decorrelation mask in real interferograms (Piton de la Fourmaise in this example), (**c**) phase unwrapping to recover ground displacements, and derive a deformation score defined as the standard deviation of the displacement map, (**d**) data dissemination, as images and time series on a public website (www.mounts-project.com), and email alerts to interested users when a threshold is overcome. Synthetic data can only seldomly cover the full range of variations and all the corner cases that can be observed in the real world, and is thus usually inferior to real data. However, there are also benefits that make it an attractive choice: with synthetic data the ground truth values of what is to be predicted are known and can be used for the training. Also, since arbitrary amounts of data can be generated, overfitting due to insufficient data is not an issue, and the generalization capability of the final model depends primarily on the realism of the synthetic data. While the present work was under review, a study using synthetic interferograms to train neural networks was published [35]. Unlike our study, the authors generate deformation patterns based on analytic models simulating realistic deformation sources in volcanic settings (i.e., Mogi and Okada sources in particular), and model stratified atmospheric effects from weather models (i.e., GACOS). This approach incorporates expert knowledge into the network via the training data, and opens pathways to potentially recover deformation sources properties from the interferogram in an automatic fashion.