# Enhanced Wind Energy Forecasting Using an Extended Long Short-Term Memory Model
## 3 SCADA Data Processing for for xLSTM
### Hyperparameter Tuning for xLSTM
#### 3.2.1 Hyperparameter Optimization for sLSTM Configuration  
For sLSTM, hyperparameter optimization focuses on maximizing the efficiency of the scalar memory mechanism and exponential gating structure. The tuning process prioritizes parameters that influence the sLSTM model's ability to revise storage decisions and facilitate  
\begin{table}
\begin{tabular}{c c c c} \hline
**Wind Direction Range** & **Raw Data** & **Outliers** & **Remaining Data** \\ \hline 0\({}^{\circ}\)–45\({}^{\circ}\) & 6314 & 401 & 5913 \\ 45\({}^{\circ}\)–90\({}^{\circ}\) & 5852 & 372 & 5480 \\ 90\({}^{\circ}\)–135\({}^{\circ}\) & 4795 & 305 & 4490 \\ 135\({}^{\circ}\)–180\({}^{\circ}\) & 5103 & 324 & 4779 \\ 180\({}^{\circ}\)–225\({}^{\circ}\) & 7128 & 453 & 6675 \\ 225\({}^{\circ}\)–270\({}^{\circ}\) & 8546 & 543 & 8003 \\ 270\({}^{\circ}\)–315\({}^{\circ}\) & 7932 & 504 & 7428 \\ 315\({}^{\circ}\)–360\({}^{\circ}\) & 4860 & 312 & 4548 \\ \hline Total & 50,530 & 3214 & 47,316 \\ \hline \end{tabular}
\end{table}
Table 2: Distribution of SCADA data by wind direction ranges.  
effective memory mixing across multiple heads. Critical parameters include the head size, which determines the dimensionality of each attention head's representation space, and the projection factor that controls the expansion ratio in the feed-forward network within each block. The number of heads per layer requires careful calibration to balance computational complexity against the xLSTM model's capacity to capture diverse temporal patterns in wind power generation data. Additionally, the initialization strategy for forget gates proves particularly crucial for stabilizing the exponential gating mechanism and ensuring consistent gradient flow during training. Hyperparameter optimization for sLSTM involves a multifaceted approach that addresses the unique architectural components of scalar memory and exponential gating mechanisms.  
A systematic grid search across parameter spaces, complemented by Bayesian optimization techniques is used for fine-tuning hyperparameters of sLSTM within promising regions, as listed in Table 3. The head size parameter demonstrated a critical inflection point at 32, with dimensions below this threshold, i.e., \((16,24)\), resulting in 7-12% higher validation errors due to insufficient representational capacity, while larger dimensions of \((48,64)\) yielded diminishing returns (less than 1.2% improvement) at substantially increased computational cost (42-78% longer training times). The projection factor of 4/3 emerged as optimal through systematic ablation studies comparing values in the range of \([1.0,1.33,1.5,2.0]\), with this specific value balancing model expressivity and computational efficiency--particularly for capturing rapid meteorological fluctuations. Additionally, forget gate initialization within the range of \([3,6]\) proved crucial for maintaining gradient stability during training, with values outside this range resulting in convergence difficulties, especially when processing long temporal dependencies characteristic of seasonal wind patterns.