Improved prediction of radionuclides sorption and diffusion in bentonite-sand mixtures using VAE-MTDL: Integrating XRF, XRD, and CEC data

Accurate predictions of the distribution coefficient ( K d ) and effective diffusion coefficient ( D e ) of radionuclides in bentonite barriers is critical for the safety evaluation of high-level radioactive waste repositories. Clay properties have a crucial impact on both parameters. However, existing models do not adequately capture the complex physicochemical characteristics of clay minerals, thereby limiting their prediction accuracy. This study developed, a variational autoencoder-multi-task deep learning (VAE-MTDL) framework to improve the predictive accuracy for K d and D e by integrating radionuclide diffusion data with X-ray fluorescence (XRF), X-ray diffraction (XRD), and cation exchange capacity (CEC) data. The model was trained using a dataset comprising 1159 experimental instances and 49 input features. It achieved high predictive accuracy (R 2 = 0.96 for Kd and 0.93 for D e ). Shapley additive explanations (SHAP) analysis identified total porosity as the most influential predictor, while XRF and XRD data significantly contributed to the predictions. Experimental validation using through-diffusion tests for HCrO 4 − (as a surrogate for monovalent anionic radionuclide species) and metal-EDTA complexes (including Eu(III), Sm(III), Ce(III), and Co(II) as a surrogate for di- and trivalent cationic radionuclide species) in compacted bentonite-sand mixtures confirmed robust generalization, with predicted-to-experimental ratios ranging from 1/5 to 5 for K d , and from 1/3 to 3 for D e . The enhanced accuracies in K d and D e predictions have practical relevance in advancing the safety evaluation of repositories.