# MoCoformer: Quantifying Temporal Irregularities in Solar Wind for Long-Term Sequence Prediction
## 4 Results
### Multivariate Results
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{**Predict Length**}} & \multicolumn{4}{c}{**Omni-Field-Magnitude Dataset**} & \multicolumn{4}{c}{**720**} \\
**Models** & \multicolumn{1}{c}{**MAE**} & \multicolumn{1}{c}{**RMSE**} & \multicolumn{1}{c}{**MAPE**} & \multicolumn{1}{c}{**MAE**} & \multicolumn{1}{c}{**RMSE**} & \multicolumn{1}{c}{**MAPE**} & \multicolumn{1}{c}{**MAE**} & \multicolumn{1}{c}{**RMSE**} & \multicolumn{1}{c}{**MAPE**} & \multicolumn{1}{c}{**MAE**} & \multicolumn{1}{c}{**RMSE**} & \multicolumn{1}{c}{**MAPE**} \\ \hline MoCoformer & **0.669** & **1.047** & **2.741** & **0.712** & **1.087** & **2.588** & **0.721** & **1.058** & **2.754** & **0.682** & **1.016** & **2.598** \\ FEDformer & 0.688 & 1.062 & 2.752 & 0.712 & 1.090 & 2.792 & 0.743 & 1.127 & 2.896 & 0.719 & 1.080 & 2.950 \\ Autoformer & 0.724 & 1.111 & 3.207 & 0.752 & 1.147 & 3.223 & 0.765 & 1.152 & 2.889 & 0.733 & 1.085 & 2.916 \\ Transformer & 0.681 & 1.084 & 3.569 & 0.716 & 1.094 & 3.151 & 0.728 & 1.102 & 2.862 & 0.690 & 1.022 & 2.687 \\ GRU & 0.693 & 1.072 & 2.978 & 0.723 & 1.096 & 3.171 & 0.747 & 1.231 & 2.798 & 0.708 & 1.069 & 2.757 \\ LSTM & 0.699 & 1.085 & 3.011 & 0.730 & 1.094 & 3.055 & 0.754 & 1.214 & 2.856 & 0.721 & 1.053 & 2.780 \\ WSA & 0.678 & 1.069 & 3.723 & 0.714 & 1.099 & 3.138 & 0.730 & 1.095 & 2.861 & 0.687 & 1.021 & 2.655 \\ \hline \multicolumn{1}{c}{} & \multicolumn{4}{c}{omni-IMF dataset} & \multicolumn{4}{c}{} & \multicolumn{4}{c}{} & \multicolumn{4}{c}{} \\ \hline Predict Length & \multicolumn{1}{c}{} & \multicolumn{1}{c}{96} & \multicolumn{4}{c}{} & 192 & \multicolumn{4}{c}{} & 336 & \multicolumn{4}{c}{} & 720 \\ Models & MAE & RMSE & MAPE & MAE & RMSE & MAPE & MAE & RMSE & MAPE & MAE & RMSE & MAPE \\ \hline MoCoformer & **0.596** & **0.850** & **2.715** & **0.628** & **0.889** & **2.593** & **0.639** & **0.894** & **2.474** & **0.628** & **0.888** & **2.415** \\ FEDformer & 0.622 & 0.897 & 2.721 & 0.641 & 0.922 & 2.791 & 0.659 & 0.950 & 2.797 & 0.644 & 0.935 & 2.661 \\ Autoformer & 0.658 & 0.932 & 2.938 & 0.650 & 0.938 & 2.814 & 0.661 & 0.948 & 2.768 & 0.641 & 0.930 & 2.597 \\ Transformer & 0.610 & 0.888 & 3.298 & 0.643 & 0.907 & 2.761 & 0.643 & 0.907 & 2.552 & 0.642 & 0.905 & 2.444 \\ GRU & 0.616 & 0.917 & 2.897 & 0.635 & 0.918 & 2.744 & 0.648 & 0.926 & 2.667 & 0.636 & 0.902 & 2.486 \\ LSTM & 0.623 & 0.930 & 2.913 & 0.644 & 0.929 & 2.781 & 0.655 & 0.930 & 2.690 & 0.645 & 0.910 & 2.483 \\ WSA & 0.601 & 0.859 & 2.954 & 0.640 & 0.896 & 2.687 & 0.644 & 0.903 & 2.492 & 0.632 & 0.896 & 2.437 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The forecasting results for multivariate 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. the highest level of performance. Remarkably, in the omni-Field-Magnitude dataset, MoCoformer surpassed the second-ranked model with an average improvement of roughly 0.76% in MAE, 1.51% in RMSE, and 3.59% in MAPE. Likewise, within the omni-IMF dataset, MoCoformer displayed an average enhancement of about 1.40% in MAE, 1.19% in RMSE, and 1.37% in MAPE compared to its closest competitor. These findings underscore the exceptional predictive power of MoCoformer in long-term sequence forecasting, showcasing its superior adaptability to temporal irregularities in solar wind sequences and resulting in more precise predictions compared to alternative models.