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

Abstract. Fault activity modelling is vital for earthquake monitoring, risk management, and early warning. Studies on laboratory earthquakes are instrumental for modelling natural fault ruptures and enhancing our understanding of natural earthquake dynamics. Recently, machine learning methods have proven effective in predicting instantaneous fault stress in laboratory settings and fault activities on Earth. However, these methods have struggled to obtain steady future predictions because of the lack of understanding of the complex dynamics of highly non-linear laboratory fault slip systems. To address this, we introduce the Hankel–Koopman autoencoder (HKAE), a novel method inspired by dynamic system theories. The HKAE performs dynamic modelling of laboratory fault systems and provides a continuous estimation of the future state of the system. It has been used in experiments with different slip behaviours and has the ability to predict shear stress variation during a slip cycle and slip activity during long-term seismic cycles. The HKAE outperforms traditional statistical methods while achieving results comparable to cutting-edge deep-learning methods across multiple prediction scales. This is particularly evident in its accurate prediction of the stress release phase and precise estimation of the slip interval. More importantly, through dynamic theory and operator analysis in latent space, the HKAE provides insights into the stability of laboratory slip systems rather than full end-to-end black-box predictions. The ability of the HKAE to decompose, model, and reveal complex temporal dynamics highlights its potential in the monitoring of sparsely observed geophysical systems with cyclic characteristics, such as natural faults.