Predicting the diffusion of CeEDTA− and CoEDTA2− in bentonite using decision tree hybridized with particle swarm optimization algorithms

The diffusion of radionuclide anionic complexes in bentonite barriers is of great concern in assessing the safety of repositories for high-level radioactive waste due to their high diffusivity. This study investigated the diffusion behaviors of CeEDTA⁻ (as surrogate to ²⁴¹AmEDTA⁻ and ²³⁹PuEDTA⁻) and CoEDTA²⁻ (as surrogate to ⁶⁰CoEDTA²⁻) in compacted bentonite using a through-diffusion method, a multi-porosity model (MP), and various decision tree algorithms hybridized with Particle Swarm Optimization (PSO). The algorithms included PSO-Light Gradient Boosting Machine (LightGBM), PSO-Categorical Gradient Boosting (CatBoost), PSO-EXtreme Gradient Boosting (XGBoost), and PSO-Random Forest (RF). The effective diffusion coefficients of these species in compacted Wyoming bentonite were determined utilizing the through-diffusion method to assess the reliability of machine learning (ML) models. The accuracy of cross validation ranked as follows: PSO-LightGBM (R_CV² = 0.91) > PSO-XGBoost (R_CV² = 0.86) > PSO-CatBoost (R_CV² = 0.85) > PSO-RF (R_CV² = 0.81). Shapley additive explanation (SHAP) and feature importance (FI) with PSO-LightGBM identified the ion diffusion coefficient in water, total porosity, and rock capacity factor as the top three features. The MP model confirmed the reliability of partial dependence plots (PDP) method, highlighting the good interpretability of ML models. This work provides an accurate, generalizable, and interpretable ML method for analyzing the adsorptive radionuclide anionic complexes diffusion in bentonite barriers.