# Enhanced Wind Energy Forecasting Using an Extended Long Short-Term Memory Model
## 4 Results and Discussion
### Discussion of xLSTM Results
#### 4.2.4 Computational Efficiency and Scalability Analysis  
While the xLSTM model demonstrates enhanced prediction accuracy, its practical deployment requires consideration of computational efficiency and scalability. The integration of multihead matrix memory structures and exponential gating mechanisms of the xLSTM model introduces additional computational complexity compared with conventional LSTM networks. Benchmark analyses on training efficiency, inference speed, and memory requirements were conducted to quantify these trade-offs. Table 8 presents the computational performance metrics of xLSTM compared with the LSTM model. Training the xLSTM model required approximately 1.3 \(\times\) the computational time of a standard LSTM network for equivalent dataset sizes, primarily due to the matrix operations in the mLSTM components. However, this increase in training time is offset by significant improvements in prediction accuracy, particularly in high wind speed regimes where accuracy is most critical for operational planning. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**Statistical Parameter**} & \multicolumn{2}{c}{**Winter**} & \multicolumn{2}{c}{**Spring**} & \multicolumn{2}{c}{**Summer**} & \multicolumn{2}{c}{**Autumnnnn**} \\ \cline{2-9}  & **SCADA** & **xLSTM** & **SCADA** & **xLSTM** & **SCADA** & **xLSTM** & **SCADA** & **xLSTM** \\ \hline Central Tendency & & & & & & & & \\ Primary Mode (kW) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ Secondary Mode (kW) & 3500 & 3500 & 3500 & 3500 & 3500 & 3500 & 3500 \\ Mean Power (kW) & 1485 & 1523 & 1326 & 1375 & 1297 & 1342 & 1186 & 1232 \\ Median Power (kW) & 876 & 907 & 742 & 788 & 823 & 865 & 693 & 745 \\ \hline Distribution Shape & & & & & & & & \\ Standard Deviation (kW) & 1356 & 1387 & 1287 & 1315 & 1183 & 1205 & 1164 & 1189 \\ Coefficient of Variation & 0.913 & 0.911 & 0.971 & 0.956 & 0.912 & 0.898 & 0.982 & 0.965 \\ Skewness & 0.632 & 0.608 & 0.745 & 0.726 & 0.587 & 0.576 & 0.824 & 0.793 \\urtosis & 1.843 & 1.814 & 1.963 & 1.938 & 1.742 & 1.726 & 2.103 & 2.072 \\ Bimodality Coefficient & 0.567 & 0.561 & 0.594 & 0.586 & 0.523 & 0.517 & 0.621 & 0.612 \\ \hline Probability Characteristics & & & & & & & & \\ Prob. Density at Primary Mode (\(\times 10^{-4}\)) & 2.20 & 4.20 & 3.50 & 5.80 & 3.80 & 5.60 & 6.50 & 6.70 \\ Prob. Density at Secondary Mode (\(\times 10^{-4}\)) & 10.20 & 9.40 & 9.20 & 8.40 & 5.90 & 6.30 & 6.50 & 2.30 \\ Prob. Power \(<\) 500 kW & 0.264 & 0.243 & 0.317 & 0.286 & 0.286 & 0.267 & 0.344 & 0.316 \\ Prob. Power \(>\) 3000 kW & 0.187 & 0.196 & 0.163 & 0.172 & 0.138 & 0.145 & 0.124 & 0.137 \\ \hline Error Metrics & & & & & & & & \\ MAPE in Probability Density (\%) & – & 5.82 & – & 7.43 & – & 6.15 & – & 8.76 \\ RMSE (kW) & – & 143.6 & – & 168.2 & – & 152.8 & – & 187.3 \\ \(R^{2}\) & – & 0.982 & – & 0.973 & – & 0.978 & – & 0.967 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of seasonal probabilistic distribution metrics for power output between SCADA measurements and xLSTM predictions. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Model** & **Training Time (min) 1** & **Inference Time (ms/Sample)** & **Memory Usage (MB)** & **Scalability Factor** \\ \hline LSTM & 4.2 & 3.5 & 186 & 1.00 \\ xLSTM [0:1] & 5.1 & 4.2 & 214 & 1.22 \\ xLSTM [1:0] & 5.6 & 4.8 & 237 & 1.28 \\ xLSTM [7:1] & 5.4 & 4.6 & 228 & 1.25 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Computational performance comparison between xLSTM and baseline models. For inference speed, the xLSTM model processes samples with an average latency of 4.6 ms on standard computing hardware, which remains well within the operational requirements for real-time wind power forecasting applications where SCADA data typically arrives at 10 min intervals. The linear computational complexity of xLSTM with respect to sequence length (\(O(n)\), where \(n\) is the sequence length) represents a significant advantage over attention-based models (\(O(n^{2})\)), particularly for extended forecasting horizons.