Continuous subsurface property retrieval from sparse radar observations using physics informed neural networks

Abstract: 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.