Discrete and continuous subsurface property retrieval from sparse radar observations using physics-informed neural networks

In various applications, ranging from environmental surveys of soils to non-destructive evaluation of infrastructure, radar sensing can be used to estimate dielectric properties (e.g., permittivity) of subsurface materials, such as soil, biomass, concrete, and asphalt. Subsurface material property can be discrete, layered, or continuously (gradually) varying. We present a physics-informed neural network (PINN)-based framework that can estimate both discrete and continuous permittivity of materials from sparse radar measurements. Unlike traditional deep learning methods, PINN satisfies both measurement data and radar physics (i.e., Maxwell’s equations) and can be trained on a very few measured waveforms. We validated the framework with both simulations and custom-built radar experiments on multi-layered natural materials. The permittivity predicted by the proposed method agrees well with the permittivity measured with an external in-situ sensor for both discrete ( R 2 ≈ 0.93) and continuous cases. The proposed PINN model can accurately predict a smoothly varying permittivity profile and even capture subtle variations in permittivity ( Δ ε 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 is applicable to scenarios with both known and unknown material layering and boundaries. It outperforms the existing model-updating approach in cases involving unknown material boundaries and limited observed data, enabling advanced electromagnetic characterization using low-cost radar systems.