## 3 Results and Discussion
### Analysis of Experimental Results  
#### 3.4.1 Results of Prediction Analysis Metrics  
To comprehensively evaluate the performance of the enhanced ChebNet model in the high-pressure physical property analysis of reservoir fluid PVT, we conducted comparative experiments between the enhanced ChebNet model designed in this paper and models such as linear regression, linear discriminant, random forest, and ordinary ChebNet. Table 3 shows the performance of each model in terms of three evaluation metrics: mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE). It can be seen from Table 3 that the enhanced ChebNet model exhibited the best performance in all three evaluation metrics. Specifically, the MAE of the enhanced ChebNet model was 0.042, which was 44% lower than that of linear regression, 32% lower than that of linear discriminant, 22% lower than that of random forest, and 12.5% lower than that of ordinary ChebNet; the RMSE was 0.056, which was 43% lower than that of linear regression, 31% lower than that of linear discriminant, 22% lower than that of random forest, and 12.5% lower than that of ordinary ChebNet; the MAPE was 4.3%, which was 45% lower than that of linear regression, 34% lower than that of linear discriminant, 23% lower than that of random forest, and 14% lower than that of ordinary ChebNet. In addition to the above comparison and analysis of MAE, MAPE, and RMSE, it was necessary to compare the prediction analysis accuracy of the ChebNet model with other models. In this part, taking the AUC metric as an example, the enhanced ChebNet model designed in this paper was compared with the AUC (area under the ROC curve) metric, which is one of the commonly used metrics for evaluating the performance of classification models and measures the ability of the classifier to distinguish between positive and negative samples, and the value range is from 0 to 1. The closer the value is to 1, the better the performance of the classifier. In the prediction comparison experiment of reservoir fluid PVT based on the ChebNet model, this paper compared the performance of several models such as linear regression, linear discriminant, random forest, ChebNet, and enhanced ChebNet in terms of the AUC metric. Figure 4 shows the experimental comparison results. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model Name** & **MAE** & **RMSE** & **MAPE** \\ \hline Linear Regression & 0.075 & 0.098 & 7.8\% \\ \hline Linear Discriminant & 0.062 & 0.081 & 6.5\% \\ \hline Random Forest & 0.054 & 0.072 & 5.6\% \\ \hline ChebNet & 0.048 & 0.064 & 5.0\% \\ \hline Enhanced ChebNet & 0.042 & 0.056 & 4.3\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of evaluation metrics of each model. 1. Linear Regression: AUC = 0.617. Linear regression is a simple linear model, and its AUC value was 0.617, indicating that its ability to distinguish between positive and negative samples is relatively weak. 2. Linear Discriminant: AUC = 0.712. Linear discriminant is a classical classification method, and its performance in the AUC metric was slightly better than that of linear regression, but was still not ideal. 3. Random Forest: AUC = 0.779. Random forest is an ensemble learning method, and its AUC value was 0.779, showing relatively good performance, but was still inferior to ChebNet and enhanced ChebNet. 4. ChebNet: AUC = 0.832. ChebNet is a model based on spectral convolutional neural networks, and it performed well in the AUC metric, better than the previous three models. 5. Enhanced ChebNet: AUC = 0.841. The enhanced ChebNet was improved compared with the ordinary ChebNet, and its AUC value was further improved to 0.841, showing the best performance. The dotted line in the figure represents the positive diagonal line, which indicates the boundary where the AUC is 0.5. Based on the comprehensive comparison of the experimental results, the enhanced ChebNet model performed best in the AUC metric.