## 4 Experimental Results and Discussion
### Comparison of Different Prediction Methods  
In this study, the dataset was divided into training and validation sets, with 80% of the samples used for the former and the remaining 20% for the latter. To stay on course, we applied several classic forecasting methods, including Informer [52], Autoformer [53], VMD-LSTM [23], and VMD-SSA-LSSVM [54]. Figure 10 shows the prediction results and the error of the three best-performing methods (Informer, Autoformer, and DFFormer). These prediction results are very close to the raw data, indicating that these methods have high accuracy and reliability in maintaining course prediction.  
In order to select the optimal prediction method among these forecasting methods, the errors between the predicted values and the raw values are calculated, as shown in Figures 11 and 12 and Table 2. The indicators in Table 2 were used to quantify the aforementioned results. Overall, DFFormer has the lowest MSE and MAE among all control variables and performs the best. In contrast, VMD-SSA-LSSVM performs the worst among all control variables, with the highest MSE and MAE. The performances of Informer, Autoformer, and VMD-LSTM fall between DFFormer and VMD-SSA-LSSVM, but are noticeably inferior to the excellent performance of DFFormer.  
These results indicate that DFFormer demonstrates higher accuracy and stability when handling these control variables, clearly outperforming other methods. This superiority is attributed to improvements in the design and training process of the DFFormer model, which exhibits a better generalization ability and prediction accuracy when dealing with complex time-series data.  
Figure 10: Prediction results with three different methods.  
Furthermore, this article also tested the running time and computational resources of DFFormer and baseline models, as shown in Table 3. These metrics include training time, inference time per prediction, and computational resources, all measured on the same hardware configuration (NVIDIA RTX 3090 GPU, 32 GB RAM).  
\begin{table}
\begin{tabular}{l l c c c c c} \hline \hline
**Phase** & **Method** & **MAE** & **RMSE** & **SMAPE** & **TIC** & **IA** \\ \hline \multirow{2}{*}{Diving} & Informer & 1.3351 & 2.2364 & 0.1395 & 0.2325 & 0.8745 \\  & Autodimer & 0.9423 & 1.3651 & 0.0712 & 0.1123 & 0.9234 \\  & VMD-SSA-LSSVM & 1.8657 & 3.9651 & 0.2654 & 0.2614 & 0.8642 \\  & VMD-LSTM & 1.1342 & 2.4362 & 0.1862 & 0.2351 & 0.8623 \\  & DFFormer & 0.7203 & 1.1235 & 0.0378 & 0.0712 & 0.9321 \\ \hline \multirow{2}{*}{Climbing} & Informer & 1.2451 & 2.2651 & 0.3751 & 0.1264 & 0.8431 \\  & Autodimer & 1.3241 & 2.8962 & 0.3241 & 0.1923 & 0.9131 \\  & VMD-SSA-LSSVM & 1.8542 & 3.1321 & 0.2074 & 0.2341 & 0.8542 \\  & VMD-LSTM & 1.5314 & 2.8621 & 0.2642 & 0.1726 & 0.8862 \\  & DFFormer & 0.8320 & 1.2368 & 0.0423 & 0.0823 & 0.9265 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Prediction errors of different methods during the diving and climbing phases.  
Figure 11: The evaluation indicators of different methods in the diving phase.  
Figure 12: The evaluation indicators of different methods in the climbing phase.  
As shown in Table 3, although DFFormer requires more training time, runtime, and storage space compared to Informer, Autoformer, VMD-LSTM, and VMD-LSTM, it is worth noting that DFFormer has higher accuracy. It can be expected that with the development of computer technology, this disadvantage of running time and storage can be further reduced. The accuracy of DFFormer can be attributed to its architecture, which combines discrete wavelet transform (DWT) for signal decomposition and fast Fourier transform-based attention (FFT-Attention) for feature extraction. These methods effectively enhance the model's ability to capture temporal features by focusing on the frequency domain, enabling DFFormer to achieve accurate predictions with stronger feature extraction capabilities. Based on the above tests, a conclusion can be drawn that DFFormer can achieve higher prediction accuracy with minimal running time and computational resources cost.