Machine-learning surrogate of the gamma buildup factor for ground-source dose conversion factors

Abstract: Dose conversion factors (DCFs) for natural radionuclides in the ground depend on the composition, density, moisture, and thickness of the source, and each new material normally requires a new Monte Carlo calculation. We propose a hybrid physics--machine-learning surrogate in which the model predicts only the effective buildup factor $\Beff$, while the uncollided dose is calculated exactly with a point kernel; the DCF of a new material is then obtained in a fraction of a second. The model uses six features computed from the photon energy, composition, density, moisture, and thickness, without any transport calculation, and was trained on 1680 Geant4 records from 70 configurations (density 0.8--2.2~g\,cm$^{-3}$, moisture 0--30\%, mass thickness 0.5--150~g\,cm$^{-2}$). Geant4 gave $\Beff$ between 1.1 and 8.6, whereas the linear buildup of the point kernel does not exceed 2. Gradient-boosted trees reduced the median error on $\Beff$ from 19.4\% to 2.2\% (1.4\% above 600~keV, close to the Monte Carlo noise), and the median error on the \iso{238}{U}- and \iso{232}{Th}-series DCFs from 4.0\% and 1.9\% to 0.9\%. On materials never used for training (Moroccan phosphate rock, phosphogypsum, calcareous soil, silica sand), the median error was 1.7\%. For 4-cm layers of Jorf Lasfar phosphate and phosphogypsum, Geant4 decay-chain calculations gave dose rates at 1~m of 217 and 148~nGy\,h$^{-1}$.