## 4 Result and Discussion
### Model Fitting Speed  
To maintain the integrity of the comparison, the number of iterations and losses were meticulously recorded for each autoencoder model throughout the training. This recording began from the initialization of training and continued at each iteration, capturing the time taken and the loss incurred until the end of the training. From Table 3, the number of iterations for the positional layer autoencoder shows significant variability, ranging from as low as 5 to as high as 48. The loss values also vary considerably, indicating fluctuations in model training performance across different runs; its average number of iterations without counting outliers is 277. The variability suggests that the positional layer autoencoder may struggle with consistency, potentially due to the complexity or non-cyclic nature of the data. The cycling 12 h autoencoder has more consistent and generally lower iteration times, with a minimum of 72 and a maximum of 255, considerably lower than the positional layer autoencoder times. The loss values are also more consistent, hovering around a narrower band. The average number of iterations of the cycling 12 h autoencoder is around 191. The cycling 24 h autoencoder also demonstrates improved consistency in the number of iterations, ranging from 81 to 210, and maintains loss values close to those of the 12 h cycling model. It has the lowest number of iterations, which is around 169 compared to the others. The 24 h cycling model is likely capturing the full diurnal cycle, which might be a strong component in the data due to natural daily rhythms in weather patterns. Table 3 enumerates the number of iterations and losses for positional, cycling 12, and cycling 24 layers. Cycling layers demonstrate a reduced number of iterations, implying faster processing than the positional layer. For instance, the cycling 24 layers exhibit the number of iterations as low as 81, whereas the positional layer's minimum of a similar loss value is 96, suggesting a more efficient training process. Thus, loss values across cycling 12 and cycling 24 are consistently lower than positional, which can imply better convergence. Table 2 suggests that cycling layers enhance speed and minimize loss, indicating a more efficient training process. Therefore, the graph infers that both cycling layer autoencoders outperform the positional layer autoencoders regarding training efficiency. This is evident from the less time for each iteration, suggesting that these models adapt to the training data more quickly. The more consistent loss values across iterations for the cycling models indicate stable learning and potentially better generalization capabilities. Additionally, Table 3 presents the loss values for different models incorporating either a positional layer or cycling layer with varying cycle lengths (12 h and 24 h). The loss value in this context typically represents the difference between the predicted values and the actual values of the time series data, measured using the Mean Squared Error (MSE) and Mean Absolute Error (MAE). These loss metrics evaluate how well the model performs, with lower loss values indicating better accuracy in the model's predictions. The table shows that models using the cycling layers (both 12 h and 24 h cycles) have consistently  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Positional**} & \multicolumn{2}{c}{**Cycling 12**} & \multicolumn{2}{c}{**Cycling 24**} \\ \hline
**Number of** & **Loss** & **Number of** & **Loss** & **Number of** & **Loss** \\
**Iterations** & & **Iterations** & & **Iterations** & **Loss** \\ \hline
485 & 98,786,208 & 176 & 98,713,768 & 169 & 98,713,792 \\
51 & 101,394,888 & 187 & 98,713,768 & 175 & 98,713,792 \\
96 & 99,171,104 & 166 & 98,713,768  
lower loss values compared to those with the positional layer, suggesting that the cycling layers are more effective at capturing long-term cyclical patterns in time series data.