Bayesian optimization for uncertainty-aware prediction of rainfall-induced deformation in embankment dams

Abstract

Abstract Reliable early warning of embankment dam failure requires predictive models that are accurate, physically consistent, and uncertainty-calibrated. This study proposes a hybrid physics-informed Bayesian deep learning framework integrating coupled u-p Biot consolidation-based finite element modeling (OpenSeesPy) with an ANN-LSTM-MDN architecture optimized via Bayesian Optimization. Deterministic hydro-mechanical responses provide physically grounded descriptors and regularization targets, while the probabilistic network decomposes uncertainty into epistemic and aleatory components. Physics-informed penalty terms enforce consolidation-consistent behavior. The approach introduces adaptive, composition-dependent uncertainty scaling to account for heterogeneous borrow materials and non-stationary rainfall effect. A novel Uncertainty Calibration Score (UCS) jointly optimizes predictive sharpness and empirical coverage. Material-adaptive dropout rates further regularize predictions for variable soil compositions. Validation on construction-phase monitoring data from the Megech Dam demonstrates substantial improvements: Negative Log-Likelihood decreased from − 2.36 to − 2.52, CRPS decreased by 33.7% ( $$0.092 \to 0.061$$ ), and PICP increased from 0.86 to 0.93. Epistemic uncertainty reduced by 37.7%, while aleatoric variability remained captured. Adaptive prediction intervals revealed a pre-failure shift, with epistemic uncertainty rising to ~ 72% of total variance 8–12 weeks before observed failure. Statistical validation via block-bootstrap resampling, paired hypothesis testing ( p  < 0.0001), and ten-fold stratified cross-validation (CV < 8%) confirms significance and stability. This framework advances embankment dam forecasting by coupling geotechnical physics with Bayesian deep learning, providing reproducible, interpretable, and uncertainty-aware early warning insights for construction-phase variability.