Fast data inversion for high-dimensional dynamical systems from noisy measurements

In this work, we develop a scalable approach for a flexible latent factor model for high-dimensional dynamical systems. Each latent factor process has its own correlation and variance parameters, and the orthogonal factor loading matrix can be either fixed or estimated. We utilize an orthogonal factor loading matrix that avoids computing the inversion of the posterior covariance matrix at each time of the Kalman filter, and derive closed-form expressions in an expectation-maximization algorithm for parameter estimation, which substantially reduces the computational complexity without approximation. Our study is motivated by inversely estimating slow slip events from geodetic data, such as continuous GPS measurements. Extensive simulated studies illustrate higher accuracy and scalability of our approach compared to alternatives. By applying our method to geodetic measurements in the Cascadia region, our estimated slip better agrees with independently measured seismic data of tremor events. The substantial acceleration from our method enables the use of massive noisy data for geological hazard quantification and other applications.

Deep Learning Forecasts Caldera Collapse Events at Kīlauea Volcano

During the three month long eruption of K\=ilauea 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 - 2.2 days. These failure events offer a unique dataset 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 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.