## 2 Materials and Methods
### Module Development
#### 2.2.3 The Learning Algorithm
A correlation coefficient of \(+1\) implies a perfect positive correlation, where an increase in one variable is associated with a proportional increase in the other variable. In contrast, a correlation coefficient of \(-1\) indicates a perfect negative correlation, where an increase in one variable corresponds to a proportional decrease in the other variable. When the correlation coefficient is 0, there is no linear relationship between the two variables. A correlation coefficient greater than 0.7 is deemed a strong correlation, implying a robust linear relationship, whereas a correlation coefficient less than 0.3 is considered a weak correlation, indicating a less pronounced linear relationship. Next, we focused on identifying the best combination of hyperparameters that would allow for low energy consumption and superior performance. Figure 7 shows the correlation matrix used to study the dependency between the different hyperparameters, energy consumption, and model prediction error, simultaneously. In the correlation matrix, the Pearson correlation coefficients between the hyperparameters, energy consumption, and _RMSE_ are indicated. It can be observed that there is a very strong correlation of 0.77 between the number of units and the energy consumption of the model, which means that an increase in the number of units per layer increases the energy consumption. Additionally, there is a moderate dependence of 0.38 between the number of hidden layers and the energy consumption of the model, implying that increasing the

Figure 7: Correlation matrix used to identify key trends. number of layers moderately increases the energy. It can also be observed that there is a weak correlation between the dropout rate and energy, indicating that an increase in dropout rate does not affect the energy consumed by the model. A relatively strong correlation of 0.58 is observed between the batch size and the prediction error, meaning that an increase in batch size will increase the error. The correlation between \(RMSE\) and the number of units per layer is \(-0.38\), so an increase in the number of layers will reduce the prediction error. It can also be observed that there is a moderate negative correlation of \(-0.28\) between \(RMSE\) and the number of hidden layers, indicating that increasing the number of hidden layers moderately reduces the error. Regarding the dropout rate and \(RMSE\), there is a weak correlation between the two parameters, so the dropout rate does not affect the prediction error. ### The Best Hyperparameters

In order to determine the optimal hyperparameters for our model, we utilized Equation (10) and examined two main criteria: minimizing energy consumption and ensuring acceptable prediction error. By varying the weight values, we were able to identify the ideal combination of hyperparameters that yielded the lowest objective function, as shown in Table 2.

From our analysis, we found that assigning equal weight values of 0.5 to w1 and w2 leads to the best combination of hyperparameters to reach the minimum objective function. This combination included three hidden layers, a batch size of 64, 184 units, the use of an RMSprop optimizer, and a dropout rate of 0.1. However, we also recognized the importance of prioritizing specific criteria depending on the goals of the model. To emphasis on minimizing energy consumption, we adjusted the weight values to w1 = 0.3 and w2 = 0.7, which led to the optimal combination of hyperparameters consisting of three hidden layers, a batch size of 64, 184 units, the use of a Nadam optimizer, and a dropout rate of 0.1. Conversely, to prioritize reducing the error in the objective function, we chose w1 = 0.7 and w2 = 0.3, which resulted in a different optimal combination of hyperparameters: three hidden layers, a batch size of 32, 72 units, the use of a Nadam optimizer, and a dropout rate of 0.1.