## 3 Experimental Setup
### Ablation Study
The integration of all modules in the full model ensures optimal feature utilization and robust generalization across datasets. Figures 7 and 8 provide visual representations of the ablation study, emphasizing the incremental improvements achieved by each module. The study underscores the complementary nature of the modules, where each component addresses distinct aspects of the learning task. The Hybrid Stress-Strain Modeling Framework enhances feature representation, Adaptive Learning with Physics-Consistency refines multi-scale feature extraction, and Iterative Error Minimization ensures structural consistency and alignment. Together, these components form a synergistic framework that significantly improves performance compared to state-of-the-art methods. The findings validate the architectural choices and highlight the robustness of the proposed approach in diverse settings. The ablation study provides crucial insights into the role of each component within the SSAPM model. Our results demonstrate that removing key modules, such as the Hybrid Stress-Strain Modeling Framework, Adaptive Learning with Physics-Consistency, or Iterative Error Minimization, leads to a noticeable degradation in performance across all evaluation metrics. The most significant drop is observed when the Hybrid Stress-Strain Modeling Framework is excluded, with the PSNR decreasing by approximately 2.23 points on the JARVIS-DFT dataset and 3.21 points on the Zenodo dataset. This confirms the fundamental role of hybrid modeling in capturing complex stress-strain relationships, as it effectively integrates mechanistic constraints with data-driven corrections. Without this component, the model struggles to generalize across diverse material conditions, leading to higher RMSE values and reduced predictive accuracy. The removal of Adaptive Learning with Physics-Consistency results in a 1.91-point drop in PSNR, indicating that the physics-informed loss functions significantly contribute to stability and robustness. Without this module, the model becomes more susceptible to overfitting, particularly when trained on smaller datasets with high variability in material properties. Similarly, omitting Iterative Error Minimization reduces SSIM by 0.026 on average, suggesting that this mechanism plays a crucial role in refining stress-strain predictions by iteratively correcting discrepancies. The AUC values also decline across all cases, further highlighting that each module contributes uniquely to the overall effectiveness of SSAPM. A deeper analysis of error propagation patterns reveals that models without the Hybrid Stress-Strain Modeling Framework exhibit increased prediction deviations in regions of high-stress concentration, especially near material defects and discontinuities. Excluding Adaptive Learning with Physics-Consistency leads to increased sensitivity to outlier conditions, suggesting that physics-informed constraints help mitigate extreme deviations. The iterative refinement process proves essential in stabilizing long-term predictions, particularly in datasets with high spatial variability. These findings underscore the importance of each model component and validate our architectural choices, reinforcing the effectiveness of SSAPM in achieving state-of-the-art performance.