A dynamic informed deep learning method for future estimation of laboratory stick-slip

Fault activities modelling holds vital importance for earthquake monitoring, risk management, and early alert. Studies on laboratory earthquakes are instrumental in the modelling of natural fault ruptures and in enhancing our grasp of natural earthquake dynamics. Recently, deep learning methods have been proven effective in predicting instantaneous fault stress in laboratory settings and slow slip events on Earth. However, these methods have struggled to conduct steady future prediction lacking grasping of the complex dynamics of highly nonlinear laboratory fault slip systems. Addressing this, we introduce the Hankel Koopman Auto-encoder (HKAE), a novel method inspired by dynamical system theories. HKAE performs dynamic modelling of laboratory fault system and provides a continuous estimation of the future state of the system. It has been deployed on experiments with different slip behaviours and shows superior ability to predict shear stress variation during a slip cycle and also slip activities in longer-term seismic cycles. The HKAE model surpasses conventional time series prediction deep learning methods, showing superior statistical evaluation metrics like RMSE and R2 with two prediction horizons. Meanwhile, we find that the HKAE can model the slip dynamics better than purely statistical modelling, as evidenced by its more accurate modelling of the slip timing, slip cycle intervals and its ability to summarize the quasi-periodic dynamics as an operator from a small number of samples to generate more robust beyond-horizon prediction. The capability of HKAE to decompose and model complex temporal dynamics highlights its potential in and sparse-observed geophysical system with quasi-periodic characteristics like natural fault activities.