PhyRestore: Physics-Structured Latent-Factor Restoration

Estimating temporal soil-loss change is challenging when physically meaningful input factors are noisy or corrupted, particularly because substantial changes are rare relative to the large number of locations exhibiting little change. We study this problem through the Revised Universal Soil Loss Equation (RUSLE) and introduce PhyRestore, a physics-structured latent-factor restoration framework. Rather than directly predicting soil-loss change or correcting a degraded physical estimate, PhyRestore restores corrupted physical factors and reconstructs temporal change through the known physical relationship. We evaluate PhyRestore in a watershed-scale bitemporal raster setting under isolated and simultaneous corruption of rainfall erosivity and cover management, comparing it with the degraded RUSLE estimate and Direct RF, XGBoost, MLP, and CNN models. Factor restoration improves high-magnitude recovery when the corrupted factors remain identifiable, but its advantage weakens under joint corruption, sparse positive extremes, and factor values outside the training support.