## 3 Proposed System
### System Management Block  
Meta-Feature Generation (MGM)  
This subsection presents the process of meta-feature generation. As introduced in Section 3.2, a meta-feature is a combination of the attributes of energy usage measurement time series. The attributes of the time series are based on statistical features such as the mean, variance, linearity, etc. Features such as kurtosis, skewness, entropy, spikiness, etc. were extracted since the time-series data that we would like to consider contain high nonlinearities and uncertainties, as depicted in Figure 2. A summary of the meta-features that we extract is given in Table 3.  
In addition to statistical features extracted from the time-series data (e.g., mean, standard deviation, skewness, kurtosis, and entropy), the MGM module also includes model-specific performance meta-features. During the offline training phase, multiple forecasting models (e.g., LSTM, GRU, CNN, Transformer) were trained on each time series, and their prediction performance was measured using metrics such as the RMSE, MAE, MSE, and RMLSE. These performance scores were then included in the meta-feature set, providing the meta-learner with rich historical context about how different models behaved on similar types of data. The model performance is measured using five metrics: the mean absolute error (MAE), mean squared error (MAE), root mean square error (RMSE) and root mean squared log error (RMSLE). These five metrics were used to measure the differences between the forecasting values and the real values. Since these metrics are errors, a smaller error means that the forecasting is more accurate. The formulas of the five metrics are as follows:  
\[\text{MAE}=\frac{1}{n}\sum_{i=1}^{n}\lvert y_{i}-\hat{y}_{i}\rvert \tag{2}\]  
\[\text{MSE}=\frac{1}{n}\sum_{i=1}^{n}\left(y_{i}-\hat{y}_{i}\right)^{2} \tag{3}\]  
\[\text{RMSE}=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\left(y_{i}-\hat{y}_{i}\right)^{2}} \tag{4}\]  
\[\text{RMSLE}=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\left(\log(1+\hat{y}_{i})-\log \left(1+y_{i}\right)\right)^{2}} \tag{5}\] \begin{table}
\begin{tabular}{l l l} \hline \multicolumn{1}{c}{**Number**} & \multicolumn{1}{c}{**Feature**} & \multicolumn{1}{c}{**Description**} \\ \hline
1 & Mean & The average value of the time series \\
2 & Variance & The variability of the time series \\
3 & Standard deviation & The spread of the time series \\
4 & Max value & The maximum value of the time series \\
5 & Kurtosis & The peakedness or tail-heaviness of the time series \\
6 & Skewness & The asymmetry of the time-series distribution \\
7 & Entropy & A measure of the complexity or disorder in the \\
8 & Linearity & Degree to which the series follows a linear pattern \\
9 & Stationarity & Degree to which statistical properties (mean, \\  10 & Missing values & The number of missing observations in time series \\
11 & Spikiness & The severity of sudden sharp peaks in time series \\
12 & Curvature & Degree of bending in the trend component \\
13 & Flat spot length & Length of straight zeros in time series \\
14 & Nonlinearity & Degree to which the time series deviates from a linear model \\
15 & Performance metrics of & Columns of the pre-trained RNN model for each \\
15 & RNN & series, including MAE, MSE, RMSE, RMLSE \\
16 & Performance metrics of & Columns of the pre-trained DNN model for each \\  17 & Performance metrics of & Columns of the pre-trained CNN model for each \\  18 & CNN & series, including MAE, MSE, RMSE, RMLSE \\
19 & Performance metrics of & Columns of the pre-trained RCM model for each \\  20 & Performance metrics of & Columns of the pre-trained Transformer model for each \\  & Transformer & each series, including MAE, MSE, RMSE, RMLSE \\  21 & Performance metrics of & Columns of the pre-trained TFT model for each \\
22 & IFT & series, including MAE, MSE, RMSE, RMLSE \\
22 & Best model & The name of the most accurate forecasting model \\ \hline \end{tabular}
\end{table} 
Table 3: The extracted meta-features and descriptions.