Deep learning-based temporal inference of hydraulic fracture length and branching using acoustic emission

Acoustic emissions (AE) have been widely employed to infer fracture growth and cracking evolution in rocks and engineered structures. This study investigates the correlation between fracture growth - characterized by fracture length and the number of branches - and AE parameters, including counts, locations, and seismic moments, using deep learning (DL) approaches. A novel strategy is proposed that leverages spatiotemporal AE inputs from a historical period ( L seconds) and a future timestep ( Δt ) to predict the incremental fracture length (IFL) and incremental number of fracture branches (INB) within each timestep. A customized DL model, termed AENet, is specifically designed to process the spatiotemporal AE inputs and predict IFL/INB, from which cumulative fracture growth metrics, including cumulative fracture length (CFL) and cumulative number of branches (CNB), are derived. Three hydraulic fracture experimental datasets from the MIT Rock Mechanics Laboratory are used to implement this DL-based correlation analysis. The results demonstrate that fracture growth exhibits a strong correlation with AE evolution, and the trained AENet model is capable of accurately predicting fracture growth from spatiotemporal AE data. Specifically, the AENet model ( Δt =1.0 s) achieves an average coefficient of determination (R 2 ) of 0.7512 and a mean relative error (MRE) of 0.3372 for CFL and CNB inference.