## 4 Methodological Approach
### The Database to Train the Networks  
The database developed referenced the city of Venice because it shares the same weather conditions with the densely populated area of Northern Italy named Po Valley. All the buildings' input parameters prone to variation in every iterative simulation are depicted in Table 1. Here, three main categories of input parameters were considered: geometry and layout, constructions and occupancy-related data. The simulations to be included in the simulation database were filtered based on the output results in order to generate realistic simulations. For instance, simulationsshowing values that were too high or too low for heating and cooling energy needs were excluded from the database, considering that the result could come from the combination of very advantageous or disadvantageous boundary conditions or building geometries and constructions. The following values were set as limits in terms of the minimum or maximum values:  
* Heating energy needs: 7/250 kWh/m\({}^{2}\);
* Cooling energy needs: 3/90 kWh/m\({}^{2}\);
* Domestic hot water preparation energy needs: 3/40 kWh/m\({}^{2}\);
* Lighting energy needs: 1/15 kWh/m\({}^{2}\);
* Other electrical appliances energy needs: 7/50 kWh/m\({}^{2}\). The building as a whole was modeled as a single zone. The average story gross height was considered to be 3 m. The building construction layers are represented in Table 2, while the glazing characteristics are shown in Table 3. The simulations also referred to indoor temperatures able to ensure average comfort conditions as specified in Table 4, whereas the schedule and internal heat gains are resumed in Table 5.  
Each iterative simulation included the parameters summarized in Table 1, with values randomly assessed via uniform sampling within predefined limits or among a set of choices given in the same table. An overall number of 600,000 simulations was run. This amount was defined based on the desired target accuracy shown by the developed ANNs. In fact, the accuracy of the ANNs depends, of course, on their architecture (e.g., the kind of network, the number of layers, the number of nodes and the chosen activation functions) as well as on the number of training records, which should be large enough to catch the related variation in the outputs, especially in the case of many degrees of freedom. Each simulation took about 5 s on a PC with an Intel Core i9 7960X microprocessor with 32 GB DDR4 RAM at 2666 MHz and an SDD hard disk. By reserving 28 threads to the simulation runs and considering the time needed to extract data from the SQLite output file, about 35 h was required to build the overall simulation database. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Code** & **Description** & **Unit** & **Range of Values** & **Notes** \\ \hline X & Length of side 1 of the floor & m & Minimum value: 7 & \\  & & Maximum value: 30 & \\ Y & Length of side 2 of the floor & m & Minimum value: 7 & \\  & & Maximum value: 30 & \\ nStoreys & Number of stories & - & Minimum value: 1 & \\  & & Maximum value: 8 & \\  & & Building’s azimuth & - & Minimum value: 0 \\ Geometry & & Window area fraction along north & & Maximum value: 90 \\ and Layout & FW,A,N & side & - & Minimum value: 0.01 \\  & & (@ Building azimuth = 0\({}^{\circ}\)) & & Maximum value: 0.90 \\  & & Window area fraction along east side & - & Minimum value: 0.01 \\  & & (@ Building azimuth = 0\({}^{\circ}\)) & - & Maximum value: 0.90 \\  & & Window area fraction along south & & Minimum value: 0.01 \\  & & side & - & Maximum value: 0.90 \\  & & (@ Building azimuth = 0\({}^{\circ}\)) & - & Minimum value: 0.01 \\  & & Window area fraction along west side & - & Maximum value: 0.00 \\  & & (@ Building azimuth = 0\({}^{\circ}\)) & - & Maximum value: 0.90 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Range of values considered in the input parameters.