## 5 Discussion  
This study systematically investigates the energy evolution characteristics (ESE and PDE) of surrounding rock in deep mining areas by integrating numerical simulation and machine learning techniques. The findings reveal the nonlinear effects of support parameters on the dynamic energy behavior of surrounding rock. The analysis demonstrates significant variations in the influence of support stiffness on elastic strain energy and plastic dissipation energy across different support designs. For instance, a moderate isotropic modulus (e.g., 25 GPa) effectively balances energy accumulation and dissipation, thereby mitigating rock damage and achieving enhanced displacement control. In terms of bolt design parameters, grout-related factors (e.g., cohesion and stiffness) play a pivotal role in minimizing energy dissipation. However, when the bolt cross-sectional area exceeds a certain threshold, energy dissipation increases instead of stabilizing, emphasizing the necessity of balancing stiffness and flexibility in support design. The findings of this study align with existing research on the optimization of support parameters and their impact on the stability of surrounding rock. For example, [PERSON] et al. [41] demonstrated through numerical simulations and orthogonal experiments that optimized support parameters, such as anchor length and spacing, significantly improved the stability of soft rock roadways. Similarly, [PERSON] et al. [42] employed a displacement control-based optimization method and highlighted the effectiveness of adjusting anchor cable length and pre-stress in controlling deformation, which corroborates this study's results showing the influence of support parameters on energy evolution in the surrounding rock. Moreover, [PERSON] et al. [43] emphasized the critical role of support parameters in controlling the plastic zone distribution in high-stress conditions, which is consistent with the energy evolution trends observed in this study. While previous research has primarily focused on plastic zone control, this study extends the understanding by incorporating the perspective of energy evolution, providing a more comprehensive framework for analyzing the effects \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods Set** & **Numerical Simulation** & \multicolumn{2}{c}{**Regression**} \\
**Training** & **Test** \\ \hline Case No. & 1 & 124 (80\%) & 31 (20\%) \\ Time/s & 90 & 1.52367 & 0.00318 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Time consumption of various calculation methods. of support design. These comparisons highlight the practical implications of optimizing support parameters for enhancing the stability of underground structures. Future work could further validate these findings through field measurements, as demonstrated by [PERSON] et al. [42], who combined numerical simulations with site observations to refine their optimization model. This approach would strengthen the applicability of the presented results in real-world engineering scenarios. Building on these findings, machine learning techniques were applied to predict energy data generated from numerical simulations. The results indicate that the decision tree (DT) model performs optimally in predicting elastic energy for support parameter designs, particularly for bolt configurations, achieving an R\({}^{2}\) value of 0.77. The support vector machine (SVM) model demonstrates superior performance in predicting dissipation energy, especially for shotcrete parameters, owing to the near-linear relationship between dissipation energy and support parameters. Additionally, the study highlights the computational efficiency of machine learning models.