## 2 Materials and Methods
### Module Development
#### 2.2.3 The Learning Algorithm
where, \(E_{c}\) and \(RMSE\) are the energy consumption and the error, respectively. Subscript u refers to the utopia solution, while max refers to the maximum values of the objective functions. The utopia solutions for this problem can be assumed to be equal to zero, where \(W_{1}\) and \(W_{2}\) are used as weights to scale and give priority to the terms. ## 3 Results and Discussion

In this section, the results of the simulation and optimization are presented and discussed. Exploiting the Influence of the Number of Units per Layer on the Energy Consumption and Performance of the Model

To exploit the influence of the number of units per layer on the energy consumption and performance of the model, we defined the range of units between 8 and 256 with a step of 8 and with a large search space of 7022 hyperparameter combinations. Figure 2a shows the evolution of the energy consumed in microjoules as a function of the number of units per layer. Each point in Figure 2a corresponds to a set of hyperparameters from the ranges defined in Table 1.

Figure 2b presents the dependence of \(RMSE\) on the number of neurons per layer. The simulation results show that a large number of units per layer increases the power consumption for training the model. However, the prediction error decreases with the increase in the number of units per layer. There is therefore a tradeoff which should be managed in such a way that energy consumption is minimized, and prediction accuracy simultaneously remains acceptable. We concluded that the number of units affects the energy consumption and the performance of the model. Thus, if the goal of the problem is to achieve the best performance, then a large number of units is the most appropriate solution. However, if power consumption is the major factor in an application, then a large number of units is unfavorable. In addition, increasing the number of units unnecessarily leads to an overfitting problem. Figure 2: (a) Variation of energy consumption as a function of the number of units per layer. (b) Variation of \(RMSE\) as a function of the number of units per layer. ### Exploitation of the Influence of the Batch Size on Energy Consumption and Model Performance

In this section, we assess the impact one of the most important hyperparameters. The goal is to determine the impact of batch size hyperparameter on the energy consumption and accuracy of the proposed deep learning model. To obtain consistent results, different values for the batch size are chosen (Table 1). Figure 3a,b summarizes the simulation results related to the impact of batch size on energy consumption and performance. We can see in Figure 3a that energy varies with the value of the batch size, and the largest value of the energy consumed by the model is for the small values of the batch size. This is due to small batch sizes require more resources (CPU and software) to see all the data and higher number of iterations. Figure 4b shows the variation of the _RMSE_ as a function of batch size. In Figure 3b, we can see that the batch size of 32 gives raise to the best result, and the large _RMSE_ values resulted in batch size values of less than 250. It is evident from these simulations that energy consumption increases with the decrease in the batch size, but the performance improves with the increase in the batch size. These results demonstrate that using a large batch size minimizes the energy but increases the prediction error of the model. From these results, we can conclude that the batch size has a significant impact on the energy consumption and performance of the model. Thus, a large batch size should be used to reduce energy consumption and achieve good model performance. ### Impact of the Number of Layers on the Energy Consumption and Performance

In order to study the influence of the hidden layers on the energy consumption and performance of our model, we changed the values of the hidden layers from two to four. Figure 4a shows the energy consumption of the model as a function of the number of hidden layers.