Ensemble Kalman Filter in a machine-learned ROM of seismic sequence

This project addresses the complex challenge of forecasting earthquake sequences by integrating physics-based modeling with state-of-the-art machine learning and data assimilation techniques. At its core, the work develops a reduced-order model (ROM) that captures the chaotic dynamics of earthquake cycles by leveraging Proper Orthogonal Decomposition (POD). By extracting the dominant spatial patterns from high-dimensional geophysical data and learning the slow/fast dynamics through neural networks, the ROM efficiently represents the essential behavior of the underlying physical processes while drastically reducing computational costs.

The reduced-order model is seamlessly integrated with an Ensemble Kalman Filter (EnKF) to assimilate sparse and noisy observational data, such as low-resolution slip rate measurements from surface observations. This combination allows the system to continuously update its state estimates and improve short-term forecasts of seismic activity. A novel time transformation approach is employed to manage the multiscale nature of earthquake dynamics, effectively decomposing the temporal evolution into parts that can be learned separately. This strategy not only enhances the model’s predictive capability but also mitigates the challenges associated with the inherent chaotic behavior of the system.

Validation against full-scale partial differential equation (PDE) simulations demonstrates that the ROM reproduces key statistical properties, including moment-duration and moment-area scaling laws, which are critical for understanding earthquake mechanics. Moreover, the data assimilation framework quantifies prediction performance in both time and space, enabling reliable forecasts of large seismic events. Overall, the project represents a significant step toward integrating machine learning with traditional geophysical modeling, offering promising pathways for improved earthquake forecasting and risk mitigation in seismology.