Predicting Apparent Diffusion Coefficient of Re(Ⅶ) Using Machine Learning With Generative Adversarial Networks

Diffusion is the predominant transportation mechanism of radionuclides in compacted bentonite, which is attributed to the low permeability, high swelling capacity, and strong adsorption characteristics. The apparent diffusion coefficient(D_a) is a crucial parameter in the safety evaluation of high-level radioactive waste repositories. However, it remains challenging to accurately predict the D_a value under complex geological conditions due to scarce experimental data and unclear diffusion mechanisms. In this study, machine learning models were employed to predict the D_a values of Re(Ⅶ) in compacted bentonites. The dataset included 1 073 experimental instances with 26 input features. Feature engineering techniques were applied to standardize the data, including outlier removal, logarithmic transformation, and max-min normalization. Data augmentation was performed using both Gaussian noise injection and the generative adversarial network(GAN) techniques, expanding the datasets to 4 292 instances with 26 input features. The influence of instance quantity on predictive accuracy was systematically analyzed, with comparative performance evaluation conducted between an integrated light gradient boosting machine-extreme gradient boosting(LGBM-XGBoost) algorithm and a deep neural network(DNN) architecture. It shows that the predictive accuracy increases with increasing quantity of instances. The predictive accuracy increases significantly after using Gaussian noise injection and GAN techniques. However, Gaussian noise injection resultes in a decrease of model robust. In addition, the LGBM-XGBoost model outperforms the DNN model in predictive accuracy, achieving a coefficient of determination(R²) of 0.99 for training set, 0.94 for validation set, and 0.94 for test sets. 95% of the instance predictions fell within a factor of 2 of the experimental values. Shapley additive explanation(SHAP) and feature importance(FI) techniques were applied in the LGBM-XGBoost model to analyze the predictive contribution of input features. It shows that the total porosity and compaction dry density are the top-two contributors. To evaluate the model’s generalization capability, through-diffusion experiments were conducted to measure the D_a values of Re(Ⅶ) in saturated compacted bentonite. The D_a values increase from 1.09×10⁻¹⁰ m²/s to 2.49×10⁻¹⁰ m²/s with decreasing compacted dry density from 1 800 kg/m³ to 1 200 kg/m³. The negative relationship between D_a and compacted dry density is consistent with the results of SHAP and FI analysis. It can be explained that the increase in total porosity facilitates Re(Ⅶ) diffusion. The LGBM-XGBoost model exhibites excellent generalization capability, with relative errors of D_a below 17%. This study establishes a potential predictive approach and mechanistic analysis tool for the safety assessment of high-level radioactive waste repositories.