A Physics-Based Digital Twin for Trail Running Race Performance Prediction: A Proof-of-Concept Study

Trail running imposes highly variable biomechanical demands due to steep, irregular terrain that renders flat-road pacing models inadequate. We present a physics-based digital twin that integrates a terrain-adaptive grade-adjusted pace (GAP) model with individualised physiological calibration to predict finish time across heterogeneous trail-running races. The GAP core applies Minetti's fifth-degree metabolic cost polynomial to map slope-dependent energy cost across the full range of uphill and downhill gradients encountered in trail racing. Segment-by-segment pace is further modulated by an altitude-VO₂max correction, a Banister TRIMP-based fatigue term, and a progressive pacing-decay factor. Course-elevation profiles are extracted from 1 Hz barometric altimeter data through a five-step normalisation pipeline. Individual parameters (sustainable VT₂ fraction α; pacing-decay slope μ) were calibrated by grid search against 13 race sessions. A sequential validation across four model-complexity stages showed R² increasing from 0.763 to 0.905. Leave-one-out cross-validation (n = 13) yielded R² = 0.864, MAE = 18.2 min, MAPE = 11.1%, and a small positive bias (+2.0 min). The framework demonstrates that integrating biomechanical terrain correction with individual physiological calibration substantially improves race-time prediction for trail running, offering a promising foundation for athlete-specific pre-race simulation.