Uncertainty-Aware Tree Root Morphology and Phenotypic Parameter Reconstructed From Ground-Penetrating Radar Signal via Physics-Informed Variational Networks

Ground penetrating radar (GPR) enables non-invasive subsurface root detection, yet existing approaches suffer from limited uncertainty quantification and poor cross domain generalization capabilities. This paper presents a physics-informed variational generative framework that integrates electromagnetic propagation principles with probabilistic deep learning to achieve reliable subsurface root characterization with principled uncertainty assessment. The framework embeds frequency wavenumber migration constraints and signal feature attribute transformation directly within a variational autoencoder architecture, enabling simultaneous three dimensional root reconstruction and uncertainty-aware prediction while achieving data efficiency through physics guided regularization. A multi-level confidence assessment strategy provides flexible decision making tools spanning from conservative high certainty detection to comprehensive coverage analysis. Comprehensive field validation against excavated ground truth demonstrates high fidelity preservation of complex root network topologies and enables systematic quantitative phenotypic parameter analysis encompassing morphological, architectural, functional, and biomass related traits. Notably, the framework exhibits robust cross domain transferability through physics-informed constraints alone, eliminating dependence on extensive labeled training data across diverse environmental conditions. This work establishes that principled integration of physical constraints with variational learning paradigms enables reliable, uncertainty-aware subsurface characterization methodologies with significant implications for forestry, ecological, and precision agriculture applications.