Estimating subsurface dielectric properties is essential for applications ranging from environmental surveys of soils to nondestructive evaluation of concrete in infrastructure. Conventional wave inversion methods typically assume few discrete homogeneous layers and require dense measurements or strong prior knowledge of material boundaries, limiting scalability and accuracy in realistic settings where properties vary continuously. We present a physics informed machine learning framework that reconstructs subsurface permittivity as a fully neural, continuous function of depth, trained to satisfy both measurement data and Maxwells equations. We validate the framework with both simulations and custom built radar experiments on multilayered natural materials. Results show close agreement with in-situ permittivity measurements (R^2=0.93), with sensitivity to even subtle variations (Delta eps_r=2). Parametric analysis reveals that accurate profiles can be recovered with as few as three strategically placed sensors in two layer systems. This approach reframes subsurface inversion from boundary-driven to continuous property estimation, enabling accurate characterization of smooth permittivity variations and advancing electromagnetic imaging using low cost radar systems.

翻译：估算地下介电属性对于从土壤环境勘测到基础设施混凝土无损评估等应用至关重要。传统的波动反演方法通常假设存在少数离散均匀层，并需要密集测量或对材料边界有较强的先验知识，这在实际属性连续变化的场景中限制了方法的可扩展性和准确性。我们提出了一种物理信息机器学习框架，将地下介电常数重建为深度的完全神经连续函数，并通过训练使其同时满足测量数据和麦克斯韦方程组。我们通过仿真及对多层天然材料定制雷达实验验证了该框架。结果显示反演结果与原位介电常数测量值高度吻合（R^2=0.93），且能敏感捕捉细微变化（Δε_r=2）。参数分析表明，在双层系统中仅需三个策略性布置的传感器即可准确恢复介电剖面。该方法将地下反演从边界驱动重构为连续属性估计，实现了对平滑介电变化的精确表征，推动了基于低成本雷达系统的电磁成像技术发展。