A Physics-Informed Online Learning Framework for Landslide Displacement Prediction

Current landslide displacement prediction models often suffer from insufficient integration between physical mechanisms and data-driven approaches, weak model generalizability, and limited operational applicability. To address these issues, this study develops a physics-informed online learning framework for landslide displacement prediction. The core of this framework is a Physics-informed Long Short-Term Memory network (Phys-LSTM). By embedding discretized forms of the stress balance, creep constitutive, and kinematic equations as hard constraints into the LSTM’s gating mechanisms and loss function, the model ensures physically consistent predictions and enhanced interpretability throughout the learning process. Leveraging real-time data streams from the Sichuan Provincial Geological Hazard Monitoring and Warning Platform, we developed an online processing pipeline for real-time multi-source data ingestion, automated quality control, spatiotemporal alignment, and physics-informed feature engineering. A progressive three-stage learning algorithm was designed to support model cold-start, incremental training, and rolling prediction. Validation across 45 model-development landslide sites and one independent application case demonstrated the framework’s significant superiority over traditional models in displacement prediction accuracy (RMSE ≤ 1.78 mm, R2 ≥ 0.96), cross-site generalization stability, and its capability to capture accelerated deformation phases. This research indicates that deeply integrating geomechanical prior knowledge into an online learning framework can effectively improve the reliability, interpretability, and operational applicability of landslide displacement prediction models, thereby providing methodological support for subsequent landslide early warning applications.