## 3 Experimental Setup
### Comparison with SOTA Methods  
The performance of our proposed method is compared with state-of-the-art (SOTA) methods on four datasets: JARVIS-DFT, Zenodo, ICME, and Materials Project. Tables 1 and 2 summarize the results across various metrics including PSNR, SSIM, RMSE, MAE, and AUC. Notably, our method outperforms existing SOTA models across all metrics, reflecting its robustness and adaptability to diverse datasets. For the JARVIS-DFT dataset, our model achieves a PSNR of 37.12, significantly surpassing the Swin-Transformer at 36.32, the second-best performer. This improvement is attributed to the multi-scale feature extraction mechanism in our method, which effectively captures structural hierarchies and enhances model resolution. Similarly, our model records the highest SSIM (0.918) and the lowest RMSE (0.044), highlighting its capacity for precise reconstruction of material properties. In terms of AUC, a critical metric for classification tasks, our approach achieves 0.935, indicating superior discriminatory power compared to the baseline models. Similar trends are observed on the Zenodo dataset, where our model demonstrates a consistent edge in PSNR (36.25) and SSIM (0.911), underlining its robustness in handling diverse datasets with varying data distributions. The ICME and Materials Project datasets further emphasize the advantages of our approach. On the ICME dataset, our model achieves a PSNR of 36.45 and an AUC of 0.928, outperformingSwin-Transformer by 1.33 and 0.013, respectively. This performance boost can be attributed to the structural consistency regularization embedded in the training loss, which ensures alignment with domain-specific properties. Additionally, on the Materials Project dataset, our method achieves a PSNR of 35.18, outperforming U-Net (34.08) and Swin-Transformer (33.87). The high SSIM (0.890) and low MAE (0.057) demonstrate our model's ability to maintain fidelity and minimize error in predictions. ```
Input: Datasets \(\mathcal{D}=\{\)JARVIS-DFT, Zenodo, ICME, Materials Project\(\}\) Output: Trained model \(\mathcal{M}_{SSAPM}\), Evaluation metrics Initialization: Set learning rate \(\eta\gets 10^{-4}\), batch size \(B\gets 64\), epochs \(E\gets 100\)  Define loss function \(\mathcal{L}=\mathcal{L}_{CCE}+\beta\mathcal{L}_{reg}\)  Initialize \(\mathcal{M}_{SSAPM}\) with random weights for each dataset \(\mathcal{D}_{i}\in\mathcal{D}\)do  Preprocess \(\mathcal{D}_{i}\): Normalize data, apply augmentations Split \(\mathcal{D}_{i}\) into training, validation, and test sets  end for forepoch \(e\gets 1\) to \(E\)do forbatch \((X,y)\in\mathcal{D}_{train}\)do  Forward pass: \(y_{\text{pred}}\leftarrow\mathcal{M}_{SSAPM}(X)\)  Compute losses: \[\mathcal{L}_{CCE}=-\frac{1}{N}\sum_{i=1}^{N}y_{i}\log(y_{\text{pred},i})\] (47) \[\mathcal{L}_{reg}=\frac{\alpha}{M}\sum_{j=1}^{M}\|\mathbf{F}_{j}-\mathbf{F}_ {j,\text{pred}}\|_{2}^{2}\] (48)  Backward pass: Update weights with Adam optimizer Adjust learning rate \(\eta\) with cosine annealing  end for  Compute validation metrics: \[\text{Precision}=\frac{\text{TP}}{\text{TP}+\text{FP}},\quad\text{Recall}= \frac{\text{TP}}{\text{TP}+\text{FN}}\] (49)  Save the best model if \(\mathcal{L}_{val}\) improves  end for for each test set \(\mathcal{D}_{test}\)do  Compute predictions \(y_{\text{pred}}\)  Evaluate metrics: \[\text{F1-score}=\frac{2\cdot\text{Precision}\cdot\text{Recall}}{\text{Precision}+ \text{Recall}}\] (50) \[\text{MSE}=\frac{1}{N}\sum_{i=1}^{N}(y_{i}-y_{\text{pred},i})^{2}\] (51) if imbalanced classesthen  Weighted Recall \(=\sum_{c=1}^{C}w_{c}\cdot\text{Recall}_{c}\) (52)  end for  end for return\(\mathcal{M}_{SSAPM}\), Evaluation metrics
```  
**Algorithm 1**Training procedure for SSAPM on material datasets  
The final performance boost can be attributed to the structural consistency regularization embedded in the training loss, which ensures alignment with domain-specific properties. Additionally, on the Materials Project dataset, our method achieves a PSNR of 35.18, outperforming U-Net (34.08) and Swin-Transformer (33.87).