Physics-informed LSTM for forecasting laboratory fault instability and its uncertainty analysis

Reliable forecasting of fault shear stress evolution is critical for understanding fault instability and mitigating seismic hazards. However, most laboratory earthquake studies focus on inferring current fault states rather than forecasting future shear stress evolution. We propose a novel physics informed long short term memory (PI LSTM) network for fault shear stress forecasting in laboratory seismic cycles. It takes ultrasonic wave speed and spectral amplitude from acoustic emission monitoring as inputs and embeds the elastic coupling relationship between the fault and the host rock into the LSTM framework to ensure mechanical consistency. We compare the PI LSTM with a purely data driven LSTM using double direct shear experimental data under four training data ratios (70%, 50%, 30%, and 10%) and quantify forecasting uncertainty via Monte Carlo Dropout. Results show that the PI LSTM performs comparably in data rich scenarios but significantly outperforms the baseline under data limited conditions. The physical constraint effectively shrinks the solution space, suppresses non physical predictions, and reduces uncertainty, as reflected by narrower 95% confidence intervals (CIs) and lower differential entropy; empirical coverage analysis further confirms the improved reliability of the physically constrained forecasts. Overall, this work transforms a black box model into a physically interpretable forecaster and offers a promising pathway toward transferring lab trained models to natural fault settings where observational data are scarce.