# Comparative Analysis of Deep Learning Methods for Real-Time Estimation of Earthquake Magnitude
## 3 Analysis of Results
### Comprehensive Comparative Analysis of Models
#### 3.1.2 Analysis of Each Model's Advantages  
The analysis that follows examines the statistical characteristics of the overall magnitude predictions for the four models depicted in Figure 3.  
DCRNN and DCRNNAmp models: In the early stage of magnitude prediction (first and second), the R\({}^{2}\) values reach 0.667 and 0.669, respectively, which are significantly higher than the 0.354 of the Exams model, indicating that these two models can provide more accurate estimates in the early stage. As the prediction time is extended, the R\({}^{2}\) values of the prediction results reach about 0.9 at 20 s, proving their reliability and accuracy in magnitude prediction. The curves of MAE and RMSE not only show the same trend, but in the early stage of the magnitude prediction, the RMSE and MAE are about 0.45 and 0.32, respectively, which are much better than those of 0.625 and 0.442 in the Exams model, which indicates that the prediction accuracy is significantly higher at each time point.  
Finally, the RMSE and MAE converge to 0.23 and 0.17, respectively, showing that the average error decreases steadily with the extension of the time window. Taken together, the DCRNN and DCRNNAmp models have significant advantages in the magnitude prediction task, providing more accurate magnitude estimates at the initial stage of prediction, and maintaining a high level of prediction accuracy with a steady decrease in the error over time, making them the best-performing models in this comparison, and can be used as the benchmark models.  
Exams model: In the early stage of magnitude prediction, the R\({}^{2}\) value is low, only 0.354, which is different from the DCRNN and DCRNNAmp models, indicating that the accuracy of early prediction is poor. As the prediction time is extended, the regression effect gradually improves and surpasses the MagNet model at 5.5 s, but the overall performance is still not as good as that of the DCRNN and DCRNNAmp models. The RMSE and MAE in the early stage are 0.625 and 0.442, respectively, which are much higher than those of the  
Figure 3: Coefficient of determination (R\({}^{2}\)), root mean squared error (RMSE), mean absolute error (MAE), and error bars for the estimation errors of the four models over time.  
DCRNN and DCRNNAmp models, indicating that there are obvious shortcomings in their prediction accuracy. Finally, the RMSE and MAE converge to 0.23 and 0.17, which are the same as the DCRNN and DCRNNAmp models, but the overall performance in the whole prediction process is inferior to the DCRNN and DCRNNAmp models.  
MagNet model: The overall performance of the regression results was average, with no outstanding R\({}^{2}\) values at any of the time points. However, it reaches the earliest stable state at about 7 s, which shows that it has some unique characteristics in terms of model stability, but this advantage is not enough to make it a better model compared to the DCRNN and DCRNNAmp models in terms of prediction accuracy and overall performance.  
In summary, the DCRNN and DCRNNAmp models perform well on several of the parameter metrics in this comparison, and are superior models for the magnitude prediction task and can be used as benchmark models; the Exams model performs poorly in terms of early prediction accuracy and overall performance; and the MagNet model, although it has the characteristic of reaching the steady state earlier, does not have as good a comprehensive performance as the DCRNN, DCRNNNN, and DCRNNAmp models. These conclusions have important reference value for further optimizing the earthquake early warning models and improving the prediction accuracy. Subsequent studies can focus on the advantageous features of the DCRNN and DCRNNAmp models, explore how to further improve their performance, and also draw on the unique features of the other models to promote the development of earthquake early warning technology.