PhySR-Bio: Multi-Stage Physics-Aware Symbolic Regression for Interpretable SAR-Based Forest Biomass Retrieval

Forest above-ground biomass (AGB) is essential for understanding forest carbon stocks and ecosystem dynamics. Despite the strong potential of synthetic aperture radar (SAR) for forest monitoring, retrieving AGB from SAR observations remains difficult because the relationship between SAR scattering responses and forest biomass is highly nonlinear, spatially variable, and often difficult to represent with both accuracy and interpretability. To address this issue, this study proposes PhySR-Bio, a multi-stage physics-aware symbolic regression framework for interpretable SAR-based forest biomass retrieval. The physics-aware design is achieved by incorporating SAR scattering-related variables, incidence angle information, and physically meaningful feature combinations into symbolic regression. Unlike black box regression models, PhySR-Bio derives an analytical formula in which the selected variables and their mathematical relationships can be directly inspected. On the independent test set, PhySR-Bio achieved an RMSE of 45.083 Mg/ha, an MAE of 33.997 Mg/ha, and an R of 0.527. It reduced RMSE and MAE by up to 6.35% and 8.57%, respectively, compared with representative semi-empirical formulas, and achieved a test RMSE within 2.3% of the best-performing black box machine learning model while retaining an explicit and interpretable expression.