A Physics-Informed Weakly Supervised Model for Multi-Source Rock Damage Evolution under Cyclic Loading

Understanding and predicting rock damage evolution under cyclic loading remains a central yet unresolved challenge, particularly when laboratory datasets are limited and commonly used damage indicators lack physical consistency. To overcome these limitations, we propose a physics-informed hybrid learning (PIHL) framework that integrates multi-source mechanical, energy, and acoustic-emission features. The framework embeds physics constraints distilled from consistent damage evolution patterns observed in the cyclic loading tests and employs an LSTM-RF hybrid architecture to fuse heterogeneous temporal features into a unified representation, thereby transforming empirical regularities into learnable supervisory signals and ensuring physically interpretable predictions. Bayesian optimization is further used to adaptively tune the model hyperparameters. The resulting fused damage variable yields physically consistent damage trajectories that align well with multi-source indicators and residual strain evolution, outperforms conventional AE-based indices, and consistently predicts the onset of residual strain acceleration well before macroscopic failure. Evaluation with four physical-consistency metrics confirms strong robustness across the tested confining pressures and loading frequencies. Overall, the PIHL framework effectively addresses the limitations of small-sample rock testing and provides a data-efficient and physically grounded approach under the tested conditions.