## 3 Triaxial Compression Calibration Test and Verification
### Training and Results of PartsNet  
This section presents the calibration results and performance of PartsNet in the aforementioned case study. In the data preprocessing of triaxial compression, GDR-Net examined the significant preset parameters of EEPA and the main contact parameters of wet sand (\(\lambda_{p}\), \(f_{s-s}\), \(f_{s-a}\), \(\Delta\gamma\), \(f_{0}\), \(r_{s-s}\), \(r_{s-a}\)). Through GDR-Net, feature dimension reduction and extraction were performed, resulting in three key parameters \(\lambda_{p}\), \(f_{s-s}\), \(f_{s-a}\) in the latent space. Figure 9 displays the loss results of GDR-Net. Reconstruction loss and KL divergence loss on the test set converged to 4.34 \(\times\) 10\({}^{-3}\) and 2.723 \(\times\) 10\({}^{-2}\), respectively, while the classification loss converged to 1.235 \(\times\) 10\({}^{-2}\). According to the principal component ordering, the relative weights of \(\lambda_{p}\), \(f_{s-s}\), \(f_{s-a}\) were found to be 0.378, 0.407, and 0.215, respectively. Therefore, \(f_{s-s}\) had the most significant impact on the experimental results, followed by \(\lambda_{p}\) and \(f_{s-a}\). We conducted 200 sets of EDEM 2022 simulations, generating \"load-displacement\" curve data, which we subsequently utilized as an input dataset for PartsNet. Using the predicted parameters from PartsNet, simulations were performed, and the calibrated curve showed a good fit with the experimentally determined curve. Figure 10 illustrates the convergence of the MSE loss and coefficient of determination (R\({}^{2}\)) during the training process. Parameter calibration can be seen as a regression prediction task, and using accuracy as an evaluation metric, as in classification problems, is not appropriate. Therefore, \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Properties** & **Bulk Material (Sand)** & **Acrylic Tube** & **Steel (Piston)** \\ \hline Poisson’s ratio & 0.3 & 0.4 & 0.3 \\ Density (g/cm\({}^{3}\)) & 2 & 1.2 & 8 \\ Young’s modulus (Pa) & 1.229 \(\times\) 10\({}^{9}\) & 5.6 \(\times\) 10\({}^{9}\) & 2.6 \(\times\) 10\({}^{11}\) \\ Coefficient of restitution & 0.25 (\(r_{s-s}\)) & 0.3 (\(r_{s-a}\)) & 0.3 \\ Coefficient of rolling friction & 0.23 & 0.22 & 0 \\ Coefficient of static friction & (0.51, 0.55) \(f_{s-s}\) & (0.38, 0.56) \(f_{s-a}\) & 0.5 \\ Tangential stiff multiplier & 0.667 & \(\backslash\) & \(\backslash\) \\ Tensile Exp & 3 & \(\backslash\) & \(\backslash\) \\ Contact plasticity ratio & (0.59, 0.79) & \(\backslash\) & \(\backslash\) \\ Surface energy (J/m\({}^{2}\)) & 1.64 & \(\backslash\) & \(\backslash\) \\ Constant pull-off force (N) & \(-\)0.002 & \(\backslash\) & \(\backslash\) \\ Particle size (mm) & 1 & \(\backslash\) & \(\backslash\) \\ Particle distribution & Dual sphere & \(\backslash\) & \(\backslash\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters of discrete element triaxial compression test. R\({}^{2}\) was used as the criterion for accuracy. In the DEM dataset used in this study, PartsNet achieved MSE convergence at 9.34 \(\times\) 10\({}^{-4}\) and R\({}^{2}\) convergence at 0.913. PartsNet incorporates additional, more thorough regression analysis evaluation metrics in addition to the fundamental evaluation metrics (loss functions and coefficient of determination) to describe the calibration performance. The specific calculation formulas can be found in Appendix A. Figure 11 illustrates the convergence of additional evaluation metrics, including the Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Median Absolute Error (MedAE), and the 0.75-quantile loss (0.75-QLoss) when Q = 0.75 during the training process of PartsNet. They converge at 0.019, 0.031, 0.011, and 0.008, respectively. Furthermore, it is worth noting that the training time of PartsNet is only 159.586 s, which will be further analyzed for its significant advantage in the ablation experiment in Section 4.2. Figure 10: Convergence results of PartsNet MSE loss and R\({}^{2}\) for triaxial test.