Physically constrained XGBoost model for pseudo-spectral acceleration prediction

Abstract

This study develops a physics-constrained ground motion model (GMM) for predicting pseudo-spectral acceleration (PSA) across 17 structural periods (0.02–4 s). Leveraging 900 seismic events from Japan’s KiK-net network, the research explicitly incorporating sensor depth and directional variability (E-W and N-S components) while employing an event-based data split to prevent information leakage. Two eXtreme Gradient Boosting (XGB) models were developed: an unconstrained model (XGB) and a novel partially constrained model (MCXGB). Unlike rigid global constraints, MCXGB enforces strict monotonicity only on source and path parameters (magnitude and distance), leaving site and depth parameters unconstrained to capture their complex, period-dependent non-linear effects. Evaluated using R² and Kling-Gupta Efficiency (KGE), both models demonstrated exceptional predictive capability (R²≈0.90, KGE≈0.92). Crucially, the MCXGB model successfully eliminated the non-physical oscillations observed in the unconstrained XGB model in sparsely sampled regions, without sacrificing statistical accuracy. Benchmarking against established empirical GMPEs further confirmed its physical reliability. The proposed MCXGB model provides a robust, interpretable, and physically consistent tool for seismic hazard assessment.