## 5 Results and Discussion
### Performance Comparison
Although LARO-XGBoost performs optimally on training data, its performance experiences a substantial decline on test data, with R\({}^{2}\) decreasing from 0.9807 to 0.9433 and RMSE increasing from 0.2694 to 0.6255, indicating certain degrees of overfitting phenomena in this model. In contrast, the EnML-LARO model demonstrates better stability. Figure 6: Strength prediction results for each model on the training set. To intuitively demonstrate the performance of various models on the test set, Figure 7 provides a visual analysis of relevant prediction results. The figure clearly shows that LARO-EnML maintains excellent prediction accuracy on the test set, with prediction points closely distributed around the ideal diagonal line. Residual analysis reveals that LARO-EnML's average bias approaches the ideal state of near-zero bias, with concentrated residual distribution. Comparatively, other models show varying degrees of performance decline on the test set, particularly the MLP model, with average bias increasing to 0.19, indicating certain generalisation limitations in single models. The comprehensive performance analysis fully demonstrates the core advantages of ensemble architecture in suppressing overfitting and enhancing generalisation capability, providing reliable technical support for predicting the strong performance of MICP-treated sand. To further validate the effectiveness of the proposed LARO-EnML model, this study also conducted a comparative analysis with other mainstream methods. Table 3 presents the performance comparison results of LARO-EnML against typical ensemble models, including CatBoost, RF, LGBM, and gradient boosting on test data. The results demonstrate that the LARO-EnML model achieves an RMSE of 0.5449, significantly lower than other \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Model Name**} & \multicolumn{4}{c}{**Evaluation**} \\ \cline{2-5}  & **RMSE** & **MAE** & **R2** & **OI** \\ \hline XGBoost & 0.7043 & 0.4028 & 0.9282 & 0.9398 \\ LARO-XGBoost & 0.6255 & 0.3446 & 0.9433 & 0.9501 \\ SVM & 1.3681 & 0.6183 & 0.7290 & 0.8173 \\ LARO-SVM & 0.6453 & 0.3409 & 0.9397 & 0.9476 \\ MLP & 0.8867 & 0.5243 & 0.8861 & 0.9125 \\ LARO-EnML & 0.5449 & 0.2853 & 0.9570 & 0.9597 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance comparison of ML models on the test set. Figure 7: Strength prediction results for each model on the test set. ensemble methods; an MAE of 0.2853, also representing the lowest value; R\({}^{2}\) reaching 0.9570, notably higher than other models; and an OI value of 0.9597, the highest among all comparative models. Additionally, Figure 8 presents prediction versus actual value comparison curves for each model, providing an intuitive visualisation. From the overall prediction trajectory perspective, EnML-LARO (bottom yellow curve) exhibits the highest degree of overlap with the actual value curve (black dashed line), particularly in peak strength regions where this model accurately captures sudden strength variation characteristics. In contrast, other models demonstrate varying degrees of prediction deviations in these critical regions. The RF model performs reasonably well in most areas but exhibits obvious underestimation phenomena at extreme value points. The LGBM model shows considerable prediction fluctuations, particularly displaying significant prediction deviations in the selected error region on the right side. CatBoost andgradient boosting performance falls between the others but still cannot match LARO-EnML in terms of accuracy. These results fully demonstrate the superiority of the proposed LARO optimisation strategy-based ensemble framework compared to traditional models in applications targeting MICP-treated sand strength modelling.