GeoPFN: subsecond geological field reconstruction with constrained uncertainty maps

Characterising spatially variable geological fields from sparse, noisy measurements remains challenging, particularly where abrupt geological contacts occur between sensors. This study presents GeoPFN, a prior-data fitted network that reconstructs clean hydraulic conductivity and pointwise predictive uncertainty from readings on irregular sensor layouts and a supplied noise level in less than a second on a GPU. Beyond the predictive mean, GeoPFN yields two constrained uncertainty maps. The structural component responds to observations and sensor geometry and can highlight incompletely sampled contacts, channels and lenses, whereas the measurement component depends on sensor layout and the supplied noise level. Evaluated on thousands of held-out fields from a synthetic geological prior, GeoPFN attained near-nominal pooled coverage with sharp predictive intervals. In paired synthetic benchmarks, it achieved better probabilistic scores and narrower intervals than kriging at similar coverage. A smaller exploratory comparison showed lower prediction error, narrower intervals and coverage closer to nominal than TabPFN-3.5. Sequential-sensing demonstrations showed that the maps can be updated rapidly as observations accumulate. These findings suggest that GeoPFN could support uncertainty-aware geotechnical site characterisation and automated survey updates.