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Measurements of volcano deformation are increasingly routine, but constraining complex magma reservoir geometries via inversions of surface deformation measurements remains challenging. This is partly due to deformation modeling being limited to one of two approaches: computationally efficient semi-analytical elastic solutions for simple magma reservoir geometries (point sources, spheroids, and cracks) and computationally expensive numerical solutions for complex 3D geometries. Here, we introduce a pair of Graph Neural Network (GNN) based elasto-static emulators capable of making fast and reasonably accurate predictions (error upper bound: 15 %) of surface deformation associated with 3D reservoir geometries: a spheroid emulator and a general shape emulator, the latter parameterized with spherical harmonics. The emulators are trained on, and benchmarked against, boundary element (BEM) simulations, providing up to three orders of magnitude speed up compared to BEM methods. Once trained, the emulators can generalize to new reservoir geometries statistically similar to those in the training data set, thus avoiding the need for re-training, a common limitation for existing neural network emulators. We demonstrate the utility of the emulators via Bayesian Markov Chain Monte Carlo inversions of synthetic surface deformation data, showcasing scenarios in which the emulators can, and can not, resolve complex magma reservoir geometries from surface deformation. Our work demonstrates that GNN based emulators have the potential to significantly reduce the computational cost of inverse analyses related to volcano deformation, thereby bringing new insights into the complex geometries of magmatic systems. 

Abstract During the 3 month long eruption of Kı̄lauea volcano, Hawaii in 2018, the pre‐existing summit caldera collapsed in over 60 quasi‐periodic failure events. The last 40 of these events, which generated Mw > 5 very long period (VLP) earthquakes, had inter‐event times between 0.8 and 2.2 days. These failure events offer a unique data set for testing methods for predicting earthquake recurrence based on locally recorded GPS, tilt, and seismicity data. In this work, we train a deep learning graph neural network (GNN) to predict the time‐to‐failure of the caldera collapse events using only a fraction of the data recorded at the start of each cycle. We find that the GNN generalizes to unseen data and can predict the time‐to‐failure to within a few hours using only 0.5 days of data, substantially improving upon a null model based only on inter‐event statistics. Predictions improve with increasing input data length, and are most accurate when using high‐SNR tilt‐meter data. Applying the trained GNN to synthetic data with different magma‐chamber pressure decay times predicts failure at a nearly constant stress threshold, revealing that the GNN is sensing the underling physics of caldera collapse. These findings demonstrate the predictability of caldera collapse sequences under well monitored conditions, and highlight the potential of machine learning methods for forecasting real world catastrophic events with limited training data.