## 3 Experimental Setup
### Ablation Study  
The ablation study evaluates the contributions of individual modules in our proposed architecture by systematically removing them and assessing performance across four datasets: JARVIS-DFT, Zenodo, ICME, and Materials Project. Tables 3 and 4 provide detailed metrics for model variants, including PSNR, SSIM, RMSE, MAE, and AUC, illustrating the impact of each module. The results confirm that each module contributes significantly to the overall performance, with the full model consistently outperforming its ablated counterparts. For the JARVIS-DFT dataset, the full model achieves the highest PSNR (37.12) and SSIM (0.918), indicating superior reconstruction fidelity and structural similarity. Removing the Hybrid Stress-Strain Modeling Framework results in a PSNR drop to 34.89, demonstrating the module's role in enhancing feature representation for material property prediction. Similarly, removing Adaptive Learning with Physics-Consistency leads to a PSNR of 35.21, slightly outperforming the model without Hybrid Stress-Strain Modeling Framework, suggesting its complementary role in refining feature extraction. Iterative Error Minimization contributes to structural alignment, as evidenced by a significant drop in SSIM to 0.894 when it is removed. Comparable trends are observed on the Zenodo dataset, with the full model achieving the best metrics, further validating the importance of the integrated modules. The ICME and Materials Project datasets reveal similar dependencies on the modular components. On the ICME dataset, the full model achieves a PSNR of 36.45 and an AUC of 0.928, indicating precise predictive capabilities and excellent classification performance. Removing the Hybrid Stress-Strain Modeling Framework reduces the PSNR to 33.76, while excluding Iterative Error Minimization results in a slightly lower SSIM (0.872), highlighting its role in maintaining visual and structural consistency. The Materials Project dataset also demonstrates the criticality of Hybrid Stress-Strain Modeling Framework, with a reduction in PSNR to 33.04 and a drop in MAE from 0.057 to 0.064 when it is excluded. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{4}{c}{**ICME Dataset**} & \multicolumn{4}{c}{**Materials Project Dataset**} \\ \cline{2-10}  & **PSNR** & **SSIM** & **MAE** & **AUC** & **PSNR** & **SSIM** & **MAE** & **AUC** \\ \hline ResNet [48] & 31.78 \(\pm\) 0.03 & 0.854 \(\pm\) 0.01 & 0.071 \(\pm\) 0.02 & 0.878 \(\pm\) 0.02 & 32.45 \(\pm\) 0.02 & 0.861 \(\pm\) 0.01 & 0.065 \(\pm\) 0.01 & 0.870 \(\pm\) 0.02 \\ EfficientNet [49] & 32.65 \(\pm\) 0.02 & 0.863 \(\pm\) 0.01 & 0.069 \(\pm\) 0.01 & 0.889 \(\pm\) 0.02 & 31.92 \(\pm\) 0.02 & 0.855 \(\pm\) 0.01 & 0.068 \(\pm\) 0.01 & 0.867 \(\pm\) 0.01 \\ U-Net [50] & 33.94 \(\pm\) 0.01 & 0.878 \(\pm\) 0.01 & 0.062 \(\pm\) 0.01 & 0.902 \(\pm\) 0.02 & 34.08 \(\pm\) 0.02 & 0.872 \(\pm\) 0.02 & 0.059 \(\pm\) 0.02 & 0.884 \(\pm\) 0.02 \\ Swin-Transformer [51] & 35.12 \(\pm\) 0.02 & 0.891 \(\pm\) 0.02 & 0.058 \(\pm\) 0.02 & 0.915 \(\pm\) 0.01 & 33.87 \(\pm\) 0.02 & 0.879 \(\pm\) 0.02 & 0.061 \(\pm\) 0.01 & 0.893 \(\pm\) 0.02 \\ MobileNet [52] & 30.87 \(\pm\) 0.02 & 0.841 \(\pm\) 0.02 & 0.078 \(\pm\) 0.01 & 0.864 \(\pm\) 0.01 & 31.24 \(\pm\) 0.01 & 0.852 \(\pm\) 0.01 & 0.073 \(\pm\) 0.02 & 0.860 \(\pm\) 0.01 \\ DenseNet [53] & 34.05 \(\pm\) 0.01 & 0.874 \(\pm\) 0.01 & 0.060 \(\pm\) 0.01 & 0.897 \(\pm\) 0.02 & 32.98 \(\pm\) 0.02 & 0.867 \(\pm\) 0.02 & 0.064 \(\pm\) 0.01 & 0.876 \(\pm\) 0.02 \\ Ours & **36.45 \(\pm\) 0.02** & **0.902 \(\pm\) 0.02** & **0.054 \(\pm\) 0.01** & **0.928 \(\pm\) 0.02** & **35.18 \(\pm\) 0.02** & **0.890 \(\pm\) 0.02** & **0.057 \(\pm\) 0.01** & **0.905 \(\pm\) 0.02** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of our method with SOTA methods on ICME and Materials Project datasets. Figure 6: Performance comparison of SOTA methods on the ICME and Materials Project datasets.