## 5 Discussion  
This study demonstrates that a multi-objective AutoML framework can effectively calibrate the key mesoscopic parameters in PFC3D simulations, achieving high accuracy for the elastic modulus of the contacts (\(E\)), stiffness ratio (\(k_{s}/k_{n}\)), and degraded elastic modulus after bond failure (\(E_{d}\)) while substantially reducing the manual tuning effort. A benchmarking ANN model was also constructed to evaluate the performance of the AutoKeras-based AutoML approach (see Appendix A). On the same testing dataset, the ANN achieved coefficients of determination (\(R^{2}\)) of 0.979 for \(E\), 0.728 for \(k_{s}/k_{n}\), and 0.575 for \(E_{d}\) (Figure 9). These results indicate that, although the ANN model offered slightly higher accuracy for \(k_{s}/k_{n}\) and \(E_{d}\), it underperformed AutoML in predicting \(E\). Importantly, the ANN's construction required extensive manual tuning of the hyperparameters, including the learning rates, hidden-layer configurations, neuron counts, and activation functions, which is both time-consuming and heavily dependent on researcher expertise [25]. In contrast, AutoKeras automates the architecture search and hyperparameter optimization [12], thereby reducing the barrier to entry for users lacking deep machine learning experience and improving reproducibility. Although the AutoML model's \(R^{2}\) values closely match those of the ANN, its streamlined workflow makes it particularly appealing for small-sample geomechanical problems where expert tuning resources may be limited. Furthermore, the literature suggests that integrating Bayesian optimization algorithms within ANN models can automate hyperparameter tuning (e.g., learning rate, number of hidden layers, neurons) [26], improving model performance and reducing manual effort. Bayesian optimization is efficient for costly, non-differentiable black-box functions like neural network training. In subsequent \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Input Variables** & **SI** & **SII** & **SIII** \\ \hline \(x_{1}\) (\%) & 0 & 0 & 0 \\ \(y_{1}\) (MPa) & 0 & 0 & 0 \\ \(x_{2}\) (\%) & 0.138 & 0.157 & 0.291 \\ \(y_{2}\) (MPa) & 43.907 & 75.383 & 95.066 \\ \(x_{3}\) (\%) & 0.271 & 0.334 & 0.525 \\ \(y_{3}\) (MPa) & 88.838 & 169 & 234 \\ \(x_{4}\) (\%) & 0.410 & 0.502 & 0.746 \\ \(y_{4}\) (MPa) & 135 & 266 & 388 \\ \(x_{5}\) (\%) & 0.532 & 0.647 & 0.954 \\ \(y_{5}\) (MPa) & 177 & 348 & 533 \\ \(x_{6}\) (\%) & 0.655 & 0.783 & 1.145 \\ \(y_{6}\) (MPa) & 217 & 420 & 661 \\ \(x_{7}\) (\%) & 0.712 & 0.785 & 1.151 \\ \(y_{7}\) (MPa) & 166 & 375 & 649 \\ \(x_{8}\) (\%) & 0.723 & 0.786 & 1.152 \\ \(y_{8}\) (MPa) & 110 & 324 & 635 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: AutoML input variables derived from experimental stress–strain curves. \begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline
**Specimen** & \(E\) **(GPa)** & \(k_{g}/k_{n}\) & \(E_{d}\) **(GPa)** & \(k_{s,d}/k_{n,d}\) & \(\sigma_{t}\) **(MPa)** & \(c\) **(MPa)** & \(\mu\) \\ \hline SI & 4.23 & 0.48 & 47.52 & 0.95 & 16.65 & 7.09 & 0.39 \\ SII & 5.23 & 0.45 & 48.85 & 1.98 & 21.09 & 11.59 & 0.64 \\ SIII & 6.03 & 0.34 & 51.63 & 1.56 & 23.44 & 16.03 & 1.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Inverted linear parallel bond model parameters for PFC3D simulations. research, we plan to compare the performance of the current AutoML model with models explicitly incorporating Bayesian optimization or similar advanced tuning techniques. Despite these relatively strong results, the overall prediction accuracy remains insufficient for some high-stakes engineering applications. For example, recent studies leveraging Convolutional Neural Networks (CNNs) or advanced ensemble methods (e.g., XGBoost) have reported \(R^{2}\) values exceeding 0.95 for comparable parameter inversion tasks [27, 28]. By comparison, the present AutoKeras-based model achieves an \(R^{2}\) of 0.710 and 0.521 for \(k_{s}/k_{n}\) and \(E_{d}\).