A distributed monitoring method for soil water content based on actively heated optical frequency domain reflectometry and physics-informed neural networks

In situ monitoring of soil water content using actively heated optical frequency domain reflectometry offers high spatiotemporal resolution. However, the accurate retrieval of soil water content from complex thermal response data remains challenging. Conventional theoretical models, limited by idealized physical assumptions, often fail to characterize heat transfer in multiphase porous media. Similarly, purely data-driven inversion methods often lack physical consistency and robustness. To address these issues, this study developed a physics-informed neural network framework validated through laboratory experiments using sand columns. The framework integrates macroscopic physical principles from asymptotic heat transfer analysis into a correlation-based loss function to mitigate measurement noise sensitivity. Specifically, the model incorporates a fixed thermal contact resistance parameter to decouple sand intrinsic properties from interface effects. This enables a submodel to determine the thermal conductivity–water content ( λ - w ) relationship without prior calibration. Experimental validation shows that the model achieves high accuracy for soil water content (R 2 = 0.92, MAE = 0.0125 cm 3 ·cm⁻ 3 ) and improved robustness compared to benchmark models. The identified λ - w function was validated against independent, ground-truth measurements of the sand’s thermal conductivity, confirming it captures the correct physical trend. This work provides a reliable approach for the distributed retrieval of water content in coarse-grained media with high physical consistency and interpretability.