Rapid Secondary Neutron Dose Estimation in Proton Accelerators Using FLUKA and Machine Learning

Proton accelerators are facilities of critical importance for radiation safety, as interactions of high-energy proton beams with matter produce secondary neutrons. In this study, neutron dose distributions were calculated using FLUKA Monte Carlo simulations for three energy levels (50, 100 and 250 MeV) across different shielding and environmental configurations (soil-air and soil-shield; along the x- and y-axes). The resulting data were predicted using machine learning models, namely Linear Regression (LR), Random Forest (RF), Gradient Boosting Regressor (GBR) and K-Nearest Neighbors (KNN). Model performance was evaluated based on the coefficient of determination (R²) and normalized root mean square error (NRMSE).The results demonstrate that along the x-axis in the soil–air configuration, GBR (R² ≈ 0.906-0.987) and RF (R² ≈ 0.833-0.988) exhibited strong performance, while in the soil-shield x-axis configuration, GBR (R² ≈ 0.762-0.797) and RF (R² ≈ 0.810-0.896) also achieved reliable predictions. Along the y-axis, GBR and RF models showed high accuracy, with R² ≈ 0.843-0.912 and R² ≈ 0.823-0.853 for soil–air, and R² ≈ 0.844-0.981 and R² ≈ 0.887-0.972 for soil-shield, respectively. These findings confirm that RF and GBR models can rapidly and reliably predict secondary neutron doses under varying energy levels and environmental conditions. The proposed hybrid Monte Carlo-Machine learning approach reduces simulation times and provides a fast and reliable method for shielding design, emerging as an effective tool for radiation safety and shield optimization in proton accelerators.