## 6 Conclusions  
This research implemented a multi-objective AutoML framework to invert three key mesoscopic parameters (\(E\), \(k_{s}/k_{nt}\), and \(E_{d}\)) of the linear parallel bond contact model in PFC3D. By generating 361 uniaxial compression simulations and extracting sixteen normalized input features from stress-strain curves, an AutoML-derived neural network was obtained. The final model achieved high predictive accuracy and robustness. Based on the results of this study, the following was concluded:  
1. Input features were normalized via Min-Max scaling, and target outputs were robustly scaled. AutoKeras automatically identified a network with two hidden layers (256 and 32 neurons, ReLU activation) that minimized a custom-weighted MSE loss across the three outputs. On the training data, \(R^{2}\) exceeded 0.98 for \(E\), 0.72 for \(k_{s}/k_{nt}\), and 0.53 for \(E_{d}\); on the unseen test data, \(R^{2}\) remained high at 0.992 for \(E\), 0.710 for \(k_{s}/k_{nt}\), and 0.521 for \(E_{d}\). These results reflect the model's ability to capture complex nonlinear mappings from stress-strain features to underlying mesoscopic parameters, particularly excelling in elastic modulus inversion. 2. A Sobol global sensitivity analysis revealed that the sixth stress sample (\(y_{6}\)) alone accounted for approximately 99.8% of the variance in the predicted \(E\), whereas \(k_{s}/k_{nt}\) was primarily influenced by the sixth strain (\(x_{6}\)) and \(y_{6}\). \(E_{d}\) inversion showed multi-variable contributions, notably from \(x_{8}\), \(x_{3}\), and \(x_{2}\), indicating that later-stage curve features are critical. To validate the practical performance, three gypsum specimens were tested, and their extracted sixteen input points were fed into the AutoML model. The inverted parameters yielded PFC3D simulations whose stress-strain curves closely matched the experimental results, confirming model reliability for real-world rock-like materials. 3. The AutoML approach reduces manual hyperparameter tuning compared to custom ANN models, achieving comparable accuracy (e.g., ANN \(R^{2}\): 0.979, 0.728, 0.575 vs. AutoML \(R^{2}\): 0.992, 0.710, 0.521) with minimal expert intervention. However, the exclusion of other influential parameters (\(\mu\), \(\sigma_{t}\), \(c\)) and only three targets limit comprehensive inversion. \(E_{d}\) prediction performance (\(R^{2}\approx 0.52\)) suggests room for improvement through richer feature extraction or additional training data. Future work should expand to all seven mesoscopic parameters, explore Physics-Informed Neural Networks(PINNs) to embed constitutive laws, and incorporate experimental noise to enhance robustness and applicability. Conceptualization, X.A. and S.H. ; methodology, X.A., S.H., Y.Z. and W.X. ; validation, Y.Z. and W.X. ; formal analysis, X.A. and W.X. ; investigation, S.H. ; resources, Y.Z. and W.X. ; data curation, X.A. ; writing--original draft preparation, X.A., Y.Z. and W.X. ; writing--review and editing, X.A., S.H., Y.Z. and W.X. ; visualization, X.A. ; supervision, S.H. ; project administration, S.H. ; funding acquisition, S.H. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China (No. 52304079), Chongqing Natural Science Foundation General Project (No. CSTB2024 NSCQ-MSX0987), Postdoctoral Research Foundation of China (No. 2024M753847), and Special Funding for Research Projects of Postdoctoral Researchers in Chongqing (No. 2023 CQBSHTB3114). Not applicable. The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author. This research was funded by the National Natural Science Foundation of China (No. 52304079), Chongqing Natural Science Foundation General Project (No. CSTB2024 NSCQ-MSX0987), Postdoctoral Research Foundation of China (No. 2024M753847), and Special Funding for Research Projects of Postdoctoral Researchers in Chongqing (No. 2023 CQBSHTB3114).