用神经网络连续重建地下介电特性，仅需少量传感器即可高精度成像。
Continuous subsurface property retrieval from sparse radar observations using physics informed neural networks
- 用物理约束的神经网络将介电常数建模为深度的连续函数。
- 实测与仿真结果吻合度高（R²=0.93），可识别Δε_r=2的微小变化。
- 适用于低成本雷达系统，适合土壤、混凝土等连续介质探测。
估算地下介电特性对环境土壤调查和基础设施混凝土无损检测至关重要。传统波形反演方法通常假设少数离散均质层，需要密集测量或强先验边界信息，在实际中因性质连续变化而受限。本文提出一种物理信息机器学习框架，将地下介电常数建模为深度的全神经连续函数，训练时同时满足观测数据和麦克斯韦方程。通过仿真与自建雷达实验在多层天然材料上验证，结果与原位测量高度一致（R²=0.93），对细微变化（Δε_r=2）敏感。参数分析表明，两层系统中仅需三个策略性布设的传感器即可准确恢复参数。该方法将地下反演从边界驱动转向连续属性估计，可精确刻画平滑介电变化，推动低成本雷达电磁成像发展。
原文摘要 · Abstract (English)
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.
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