Physics-Informed Machine Learning for Spatial Radon Diffusion Length Modelling Across Georgia

Radon is a naturally occurring radioactive gas produced by the decay of uranium in soil and rock. It is the second-leading cause of lung cancer after smoking, and because it is colorless and odorless, the only way to assess risk in a given location is to model how it moves through soil and into buildings. A central physical quantity governing this process is the radon diffusion length: the average distance a radon atom travels through soil before decaying, which in turn determines the barrier thickness required for effective mitigation. Existing estimation methods rely on fixed-site field deployments, physical sensor testbeds instrumented with radon, soil moisture, and temperature sensors that produce accurate local estimates but do not generalize: diffusion length depends nonlinearly on soil moisture, temperature, and porosity in ways that vary by location and season, and deploying dense sensor networks at scale is prohibitively expensive. We frame closing this gap as a spatial regression problem. Using an established physical diffusion model, we compute diffusion-length labels from environmental sensor data (soil moisture, temperature) at 14 monitoring stations distributed across the U.S. state of Georgia, paired with regional soil property data, and train ensemble regression models (Random Forest, XGBoost) augmented with physics-informed features and monotonic constraints derived directly from the governing equation. Under leave-one-station-out cross-validation, the physics-informed model substantially outperforms unconstrained baselines, confirming that encoding known physical structure improves spatial generalization to unseen locations. We further validate against an independent, real-world sensor deployment excluded from training, which reveals a structural limitation of tree-based ensembles when extrapolating beyond the range of values seen during training, a finding we discuss alongside a proposed hybrid strategy that falls back to the physical model outside the learned model's valid range. Ongoing work incorporates additional geological covariates bedrock lithology, equivalent uranium content, and soil permeability as proxies for radon source strength to complement the transport-focused diffusion model with a more complete picture of spatial radon risk.