## 4 Simulation and Results  
The MLP and SVR networks are designed to predict the cooling and heating load. Each of these networks was trained using a dataset as input. In this paper, 85% (658 samples) of the data were used to train and validate the proposed methods and the remaining 15% (110 samples) were used for testing. In the first stage, each network required a preliminary design to determine the number of neurons in the hidden layer and the coefficients of the network. After designing each network, the amount of training and testing data for the network was determined. In this work, 70% of the samples were considered as training data and 30% as test data to validate the training phase of each network. After training and testing each neural network or regression algorithm, the results need to be evaluated. To do this, correlation coefficient (R), mean squared error (MSE), root mean squared error (RMSE), and mean absolute error (MAE) can be used as statistical performance metrics. Each of the mentioned indices are calculated according to the following equations [42]. \[R=\frac{\sum\limits_{l=1}^{N}{(x_{l}-\overline{x})(y_{l}-\overline{y})}}{ \sqrt{\sum\limits_{l=1}^{N}{(x_{l}-\overline{x})^{2}\sum\limits_{l=1}^{N}{(y_ {l}-\overline{y})^{2}}}}} \tag{8}\]  
\[RMSE=\sqrt{\frac{1}{N}{\sum\limits_{l=1}^{N}{(x_{l}-y_{l})^{2}}}} \tag{9}\]  
\[MSE=\frac{1}{N}{\sum\limits_{l=1}^{N}{(x_{l}-y_{l})^{2}}} \tag{10}\]  
\[MAE=\frac{1}{N}{\sum\limits_{l=1}^{N}{\left|{x_{l}-y_{l}}\right|}} \tag{11}\]  
where \(x_{l}\) and \(y_{l}\) illustrate the actual value and predicted value. \(\overline{x}\) and \(\overline{y}\)\(\overline{y}\) depict the mean of actual values and forecasted values, respectively. Figure 3 shows the good correlation coefficient between the real values and the predicted value by the network in the training, testing and validation steps for the MLP network. Figure 4 indicates an excellent correlation coefficient between the real values and the predicted value for the SVR network during the training phase. Given the excellent correlation between the target data and the output of each network (as shown in Figures 3 and 4), it can be clearly understood that each of these networks have passed the training phase well. Good training means that the network is able to identify inherent patterns in the nature of data and to predict the unknown data by using the learned patterns, so that each network learns how much of a cooling and heating load is required for each building with specific characteristics. With this training, each network can predict the amount of cooling and heating loads related to the input data of the test phase. After training, each network is validated using initial test data (30% of 85%). This is kind of a test for the training phase, which is done by the network itself. The prediction error in the test or validation, which is one of the most important values in evaluating the results, is presented in Figures 5 and 6 for each of the MLP and SVR networks in the histogram form, respectively. The error obtained in the error histogram model indicates the minimum and maximum prediction error. This means that in predicting the cooling and heating loads for the test data, the amount of error that each of the trained networks can have is equal to the amount provided in the above figures. In evaluating and analyzing each of the above figures that somehow represent the performance of each network in the initial training and testing stages, it can be concluded that the training of proposed methods has been well validated using the desired data. It should be noted that when the network is trained with high accuracy, it is well designed and the amount of error in the validation and initial  
Figure 5: MLP testing error in the for histogram; (**a**) heating load; (**b**) cooling load. Figure 6: SVR testing error in the for histogram; (**a**) heating load; (**b**) cooling load. Figure 7: Heating load forecasting via MLP and SVR.