# MoCoformer: Quantifying Temporal Irregularities in Solar Wind for Long-Term Sequence Prediction
## 4 Results
### Univariate Results  
Table 2 compiles univariate prediction evaluation results for various methods on the two solar wind time series datasets. Experimental settings maintain a fixed input length of 96, with prediction lengths at 96, 192, 336, and 720 for training and evaluation. The research presents the evaluation results of MAE, RMSE, and MAPE metrics across different models and prediction horizons. MoCoformer demonstrated superior performance across a range of prediction horizons. Specifically, on the omni-Field-Magnitude dataset, MoCoformer exhibited a performance boost of around 2.16% in MAE, 1.92% in RMSE, and 2.30% in MAPE compared to the second-ranked model. Likewise, on the omni-IMF dataset, MoCoformer showcased a significant improvement of about 13.54% in MAE, 4.27% in RMSE, and 10.36% in MAPE over the second-ranked model. These results highlight the exceptional predictive capabilities of MoCoformer in long-term sequence forecasting. To validate the effectiveness of the proposed model in long-term solar wind sequence prediction applications, a comprehensive case study is conducted. Figure 6 illustrates the visual results of univariate prediction experiments conducted on the omni-Field-Magnitude dataset, showcasing comparisons between the outputs of multiple models and ground truth curves. This experiment aims to evaluate the predictive capability and accuracy of the proposed model in real-world applications. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multicolumn{10}{c}{**Omni-Field-Magnitude Dataset**} \\ \hline \hline
**Predict Length** & \multicolumn{3}{c}{**96**} & \multicolumn{3}{c}{**192**} & \multicolumn{3}{c}{**336**} & \multicolumn{3}{c}{**720**} \\
**Models** & **MAE** & **RMSE** & **MAPE** & **MAE** & **RMSE** & **MAPE** & **MAE** & **RMSE** & **MAPE** & **MAE** & **RMSE** & **MAPE** \\ \hline MoCoformer & **0.699** & **0.926** & **2.408** & **0.711** & **0.968** & **2.156** & **0.731** & **0.988** & **1.983** & **0.733** & **0.968** & **1.850** \\ FEDformer & 0.726 & 1.020 & 2.815 & 0.742 & 1.045 & 2.589 & 0.776 & 1.070 & 2.678 & 0.792 & 1.057 & 2.614 \\ Autoformer & 0.782 & 1.047 & 3.119 & 0.776 & 1.065 & 2.727 & 0.774 & 1.057 & 2.742 & 0.792 & 1.057 & 2.614 \\ Transformer & 0.714 & 0.954 & 2.612 & 0.725 & 0.986 & 2.258 & 0.758 & 1.009 & 1.997 & 0.739 & 0.987 & 1.897 \\ GRU & 0.736 & 0.978 & 2.758 & 0.749 & 0.994 & 2.534 & 0.762 & 1.037 & 2.179 & 0.788 & 0.993 & 1.985 \\ LSTM & 0.743 & 0.983 & 2.745 & 0.748 & 1.032 & 2.629 & 0.767 & 1.044 & 2.295 & 0.794 & 1.006 & 1.996 \\ WSA & 0.753 & 0.970 & 2.440 & 0.760 & 1.003 & 2.402 & 0.784 & 1.023 & 2.036 & 0.758 & 0.975 & 1.905 \\ \hline \multicolumn{10}{c}{omni-IMF dataset} \\ \hline \hline Predict Length & \multicolumn{3}{c}{96} & \multicolumn{3}{c}{192} & \multicolumn{3}{c}{336} & \multicolumn{3}{c}{720} \\ Models & MAE & RMSE & MAPE & MAE & RMSE & MAPE & MAE & RMSE & MAPE & MAE & RMSE & MAPE \\ \hline MoCoformer & **0.583** & **0.812** & **2.128** & **0.588** & **0.860** & **2.464** & **0.594** & **0.865** & **2.316** & **0.607** & **0.833** & **2.471** \\ FEDformer & 0.650 & 0.851 & 2.528 & 0.669 & 0.968 & 2.643 & 0.657 & 0.967 & 2.965 & 0.660 & 0.985 & 2.771 \\ Autoformer & 0.632 & 0.935 & 2.574 & 0.649 & 0.956 & 2.633 & 0.639 & 0.955 & 2.722 & 0.667 & 0.891 & 2.795 \\ Transformer & 0.628 & 0.931 & 2.450 & 0.660 & 0.963 & 2.570 & 0.652 & 0.969 & 2.535 & 0.628 & 0.950 & 2.999 \\ GRU & 0.624 & 0.896 & 2.385 & 0.637 & 0.902 & 2.586 & 0.651 & 0.913 & 2.602 & 0.668 & 0.922 & 2.684 \\ LSTM & 0.633 & 0.917 & 2.527 & 0.641 & 0.934 & 2.599 & 0.657 & 0.954 & 2.671 & 0.674 & 0.957 & 2.767 \\ WSA & 0.642 & 0.930 & 2.287 & 0.658 & 0.943 & 2.610 & 0.641 & 0.939 & 2.900 & 0.658 & 0.965 & 2.964 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The forecasting results for univariate long-term series, with an input length of I = 96 and prediction lengths of O \(\in\) [96, 192, 336, 720]. Lower values of MAE, RMSE, and MAPE indicate better performance, and the optimal results are highlighted in bold.