## 4 Methodological Approach
### ANN Training and Accuracy Improvement  
In order to address the research question, in this study, the authors suggested using deep feedforward artificial neural networks (DFANNs). These are versatile nonlinear algorithms capable of understanding highly complex relationships between a set of inputs and a set of outputs, consequently building reliable forecasting functions. Even though they are able to correlate multiple input variables to multiple output variables, they have been used in this paper to correlate multiple input variables to one output at a time. This way, a high level of accuracy could be achieved with relatively simple DFANNs, also guaranteeing fast computation sessions. DFANNs, trained by means of the backpropagation (BP) algorithm, constitute the main category of ANNs in such regression analyses. In fact, even if the dynamic thermal behavior of the building is accounted for in the frame of each simulation, the results in each data record should be seen as a single value with no need to resort to recurrent neural networks (RNNs), which are typically used in the forecasting of time series. The development of the DFANNs was conducted through the minimization of the overall difference between the predicted output values (ANN forecasts) and the true values (expected values). This process was performed using the mean squared error loss function. In particular, the development of the DFANNs was an iterative process, cycling the \"training\" and \"testing\" phases in what it is usually named an epoch in order to minimize the result of the loss function. During the \"training phase\", the training dataset was used to refine the architecture of the network so as to decrease the value of the loss function in comparison with the assessment developed in the previous epoch. However, since the training process was used to change the network characteristics according to the training dataset, the DFANNs could get too close to the training values, therefore giving a very accurate prediction of all of the output values contained in the training datasetbut a weak estimate if applied to other samples, such as the ones constituting the \"test dataset\". This would be verified if the value of the loss function increased when calculated on the \"testing dataset\", but it still decreased if it was calculated on the \"training dataset\". This phenomenon is named overfitting, and it shows that the considered DFANNs lacked generalization properties. Afterward, during the \"testing phase\", the test dataset was used to calculate the loss function after the modification to the ANN architecture happened in the training phase. The accuracy of the DFANNs mainly depended on the number and on the distribution of the available records for training and testing, and it also depended on the complexity of the model (i.e., the number of nodes and layers). Regarding the number and distribution of the available records for training and testing, the higher the number, the better the accuracy. However, any simulation costs running time, and wide datasets increase the time needed to train the DFANNs. Thus, to keep the number of simulations as low as possible, this number was progressively increased until the DFANNs showed better results for the unknown samples. The proper size of the training and testing dataset was defined to be 600,000 samples. Conversely, with regard to the complexity of the model, we cannot state that the higher the complexity, the better the accuracy. In fact, too many layers and nodes may result in excessive degrees of freedom in a DFANN and hence a decrease in its generalization capability, therefore leading to overfitting problems. In order to identify the best complexity of the model, DFANNs were developed in series. This means that many DFANNs were developed corresponding to various complexity levels by means of a parametric approach. Finally, after the most suitable complexity of the model was identified, an additional trick was used: the ensemble approach.