Physics-Guided Gaussian Process Mapping of Strong-Gradient Radiation Fields from Mobile Robot Surveys: The Role of Sampling Geometry.

Radiation fields around collimated or shielded sources exhibit strong gradients whose accurate delineation is critical for worker protection and emergency response. Mobile robots can survey such fields, but they sample sparsely and irregularly along their trajectories, and it remains unclear which reconstruction method can be trusted, and where. Using a single dominant collimated source in a two-dimensional indoor setting, this study shows that the answer depends decisively on sampling geometry, and proposes a physics-guided Gaussian process (GP) that performs reliably under trajectory-constrained sampling. A tracked robot combining light detection and ranging (LiDAR)-based simultaneous localization and mapping (SLAM) with a γ dose-rate detector surveyed a collimated Cs-137 field in seven independent runs, and all methods were evaluated under both random hold-out (interpolation near visited locations) and spatial block cross-validation (extrapolation into unvisited regions); truth-referenced evaluation against a dense reference field is provided by Poisson-sampled simulations, while experimental accuracy is cross-validated on held-out measurements. Under uniform sampling, a multilayer perceptron (MLP) robustly outperformed GP variants (R2=0.95, stable across 18 seed combinations); under trajectory sampling, its advantage vanished at visited locations and reversed catastrophically in unvisited regions. The proposed physics-guided GP, which uses a fitted collimated-beam template as the GP mean with a Matérn 3/2 residual process, achieved the highest extrapolation R2 (median 0.61; best baseline 0.31), reduced the extrapolation error by 32-69% relative to all eight baselines, recovered interpretable source parameters, and provided predictive intervals with approximately calibrated region-level coverage (point-wise error ranking remains weak); a runtime fit-quality gate further renders the correctness of the embedded prior an observable quantity, so the method flags when its own assumptions fail. These results offer quantitative guidance for method selection in robotic radiation mapping under the as low as reasonably achievable (ALARA) principle.