The predicted versus actual Kd plot compared six modeling approaches: HOP-RSM, GB, Linear HOP-RSM-GB, RMSE-based HOP-RSM-GB, Multiplicative HOP-RSM-GB, and Meta HOP-RSM-GB shown in Figure and data for the models is given on Table . The distribution of points around the ideal y = x line revealed distinct differences in predictive accuracy among these models. The meta-model (Meta HOP-RSM-GB) exhibited the highest alignment with the ideal line, achieving an R 2 of 1.00, RMSE of 10.59, MSE of 112.21, and MAE of 3.95. This indicated near-perfect predictive performance due to the ensemble's ability to capture both global trends and local variations in adsorption behavior. The hybrid HOP-RSM with GB model had the highest predictive accuracy and least error values compared to stand-alone models, hybrid QRSM models, and hybrid HOP-RSM with RF and XGB models as shown in Table . The predicted vs actual Kd plots for the other 5 hybrid models are shown in Figures S1, S2, S3, S4, and S5.