Predicting element concentrations by machine learning models in neutron activation analysis

Applications for machine learning (ML), deep learning, and other artificial intelligence models have shown great promise in nuclear physics, including not only in classification systems but also in the analysis of numerical data. This study used various ML algorithms to estimate the concentrations of six rare earth elements (Sm, La, Ce, Sc, Eu, and Tb) in both archaeological and marine sediment samples. An interesting aspect of this analysis is that 80% of the 235 data points were used for training data, which included two parameters: specific activity (Asp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A}_{{\text{sp}}}$$\end{document}) and concentration (rho\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho $$\end{document}) by the k0-method for the purpose of model development. The remaining 20% of the dataset was held out for testing the model's accuracy. The fundamental principle of this approach is the use of regression analysis between Asp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A}_{{\text{sp}}}$$\end{document} and rho\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho $$\end{document} to construct a machine learning regression model. This machine learning model was subsequently applied to estimate element concentrations based on Asp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A}_{{\text{sp}}}$$\end{document} values obtained from gamma spectra. The mean absolute error (MAE), root mean square error (RMSE) and the statistical measure R-squared (R2) were employed for evaluating the accuracy of the predicted models. The random forest (RF) algorithm produces smaller MAE and RMSE values and achieves better R2 values compared to other algorithms. In addition, RF shows the lowest relative bias of the concentration values of elements in reference material (NIST 2711a) compared to other prediction models. The work focuses on demonstrating that machine learning models can effectively predict the concentrations of rare earth elements, even though this is a fundamental issue in NAA and one previous study has addressed this issue for one single element. The extension of the current work and potential directions for further development will be presented in the results and discussion section.