## 4 Results
### Model Performance Evaluation and Comparison  
The study quantitatively evaluates the self-prediction performance of each model based on the prediction results of multiple models and selects the deterministic coefficient (R\({}^{2}\)), the adjusted deterministic coefficient (Adj.R\({}^{2}\)), the mean absolute percentage error (MAPE), the mean absolute error (MAE), the root-mean-square error (RMSE), and the variance accounted for (VAF), a total of six statistical indexes, to evaluate the comprehensive performance of each model. The generalization ability of the models is reflected more comprehensively and objectively by these indicators. Equations (38)-(43) are the mathematical definitions of these indicators [38; 39]. R\({}^{2}\) measures the ability of the model to explain the target variable and takes the value of [0,1]. \[R^{2}=1-\frac{\sum_{i=1}^{n}{(y_{i}-\hat{y}_{i})^{2}}}{\sum_{i=1}^{n}{(y_{i}- \overline{y}_{i})^{2}}} \tag{38}\]  
Figure 6: Fitted plot of predicted results. where \(y_{i}\) is the actual value, \(\hat{y}_{i}\) is the predicted value, \(\overline{y}\) is the mean of the actual value, and \(n\) is the number of data points. Adj.R\({}^{2}\) takes into account the effect of the number of independent variables on R\({}^{2}\). \[Adj.R^{2}=1-\frac{(1-R^{2})(n-1)}{n-k-1} \tag{39}\]  
where \(k\) is the number of independent variables. MAPE is used to measure the percentage of prediction error relative to the actual value with the formula  
\[MAPE=\frac{1}{n}\sum_{i=1}^{n}\left|\frac{y_{i}-\hat{y}_{i}}{y_{i}}\right| \times 100\% \tag{40}\]  
MAE is the average of the absolute values of all prediction errors:  
\[MAE=\frac{1}{n}\sum_{i=1}^{n}\left|y_{i}-\hat{y}_{i}\right| \tag{41}\]  
The RMSE reflects the mean square error between the predicted and actual values and is given by the following formula:  
\[RMSE=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\left(y_{i}-\hat{y}_{i}\right)^{2}} \tag{42}\]  
VAF is an indicator of variance explanatory power with the formula  
\[Var=(1-\frac{Var(y_{i}-\hat{y}_{i})}{Var(y_{i})})\times 100\% \tag{43}\]  
where Var denotes the variance. Radar diagrams are plotted based on the results of the calculations of the predictive performance of each model in Table 2 and are shown in Figures 7 and 8.  
but still achieves R\({}^{2}\) and VAF values of 0.97 and 97.38%, respectively, on the test set, outperforming other comparative models. In contrast, traditional models (such as LightGBM, MLP, and SVR) show acceptable performance on the training set but experience a significant decline on the test set, with R\({}^{2}\) and VAF dropping below 0.90 and 90%, respectively. Their error metrics (RMSE, MAE, MAPE) also increase notably, indicating weaker generalization capabilities and a tendency to overfit. The superior performance of the IBKA-CNN-Transformer model is largely due to the advantages of the Transformer structure in multi-dimensional feature extraction and complex relationship modeling. In particular, the multi-head self-attention mechanism is able to efficiently capture the global dependencies between multi-dimensional input features and mine their potential higher-order interaction patterns by assigning dynamic attention weights to each input feature. This mechanism is able to extract feature representations from multiple subspaces in parallel, which makes the model performance more flexible and robust in the face of complex nonlinear data. The feed-forward neural network module further enhances the feature representation capability through nonlinear transformation, enabling the model to capture complex and implicit feature patterns in the input data. At the same time, residual concatenation and layer normalization ensure the stability of the deep network during the training process, effectively mitigating the gradient vanishing problem. These features enable the Transformer model to achieve a significant improvement in global modeling capability, and combined with the local feature extraction  
Figure 8: Radar chart of test set prediction results.