Physics-Guided Hydrodynamic Clustering and Probabilistic Prediction of Dam-Break Wave Run-Up in Confined Channels

Reliable probabilistic prediction of dam-break wave run-up is important for screening downstream barriers and river infrastructures. However, it remains unclear whether propagation conditions exhibit stable statistical groups within the observed predictor domain and whether explicitly incorporating these groups improves prediction beyond the underlying continuous variables. This study develops a probabilistic framework integrating physics-guided self-tuning spectral clustering (PG-STSC), quantile regression forests (QRFs), and conformal calibration diagnostics. The framework was applied to 155 physical model observations characterized by relative propagation distance, Froude number, relative wave height, relative wavelength, and wave nonlinearity, with the relative maximum run-up as the response variable. Full-data PG-STSC identified two groups containing 66 and 89 observations, separating mainly shorter-distance, higher-Fr conditions from longer-distance, lower-Fr conditions. The partition showed moderate physical-space separation but high subsample stability, while the group-wise run-up distributions overlapped substantially. In fivefold out-of-fold evaluation, the group-free QRF achieved a continuous ranked probability score (CRPS) of 0.1537, corresponding to 22.8% CRPS skill relative to the unconditional empirical distribution. Global and group-conditioned conformal corrections produced identical pooled 90% coverage (0.942) and interval widths, with group-specific coverages of 0.922 and 0.952, respectively. Supported-domain exceedance maps translated the predicted conditional distributions into threshold screening information while masking unsupported extrapolation. Overall, physically coherent clustering improves interpretation and conditional diagnostics but does not necessarily enhance predictive performance. The resulting exceedance estimates are suitable for within-domain scenario screening rather than site-specific overtopping assessment.