## 7 Conclusions  
This paper deals with the generation of a set of artificial neural networks as a means to automatically assess the building energy demand from the very early design stages of a project, even in the case of interactive input/output frameworks, without the need of using any dynamic energy simulation software.  
The work started from the construction of a very large database of 600,000 instances, which resulted from dynamic building energy simulations in EnergyPlus. This database was employed to train and test the set of deep feedforward artificial neural networks within an iterative process, aimed at increasing the overall accuracy of the networks. For this purpose, some additional robust techniques were also employed, such as the power transformation and ensemble approaches.  
Despite the large number of input parameters, as well as their wide value ranges, the combination of these algorithms and techniques made it possible to achieve very high accuracy during the testing procedures, with errors below 5% for over 99.5% of the testing dataset, thus confirming the very high reliability and generalization capabilities of the networks.  
The developed set of ANNs is therefore proposed as a reliable substitute for dynamic building energy simulation software in the design of ZEBs during the early design stages. Further steps of this work will focus on the development of similar DFANNs for building zones to allow the designer to extend the flexibility in designing complex buildings.  
Conceptualization, M.P., M.S., A.G.R., L.G. and L.S.; methodology, M.P., M.S. and A.G.R.; software, M.P. and M.S.; validation, M.P. and M.S.; formal analysis, M.P., M.S., A.G.R. and L.G.; investigation, M.P., M.S. and A.G.R.; resources, M.P. and M.S.; data curation, M.P., M.S. and A.G.R.; writing--original draft preparation, M.P., M.S. and A.G.R.; writing--review and editing, M.P., M.S., A.G.R. and L.G.; supervision, M.S. and L.S.; project administration, M.S.; funding acquisition, M.S. and L.S.. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Code**} & \multirow{2}{*}{**Zone**} & \multirow{2}{*}{**Floor**} & \multirow{2}{*}{**North Fagade**} & \multicolumn{2}{c}{**East Fagade**} & \multicolumn{2}{c}{**South Fagade**} & \multicolumn{2}{c}{**West Fagade**} & \multicolumn{2}{c}{**Heating Energy**} & \multirow{2}{*}{**Heating Energy**} & \multirow{2}{*}{**Error**} \\  & & & **Area** & & & & & & & & & **(by ANN)** & **(Simulated)** \\ \hline  & m\({}^{2}\) & m\({}^{2}\) & m\({}^{2}\) & m\({}^{2}\) & m\({}^{2}\) & m\({}^{2}\) & m\({}^{2}\) & m\({}^{2}\) & kWh/m\({}^{2}\)–y & kWh/m\({}^{2}\)–y & \% \\ \hline Building a & Padua & 144 & 69 & 25 & 40 & 0 & 69 & 14 & 40 & 0 & 14.4 & 13.90 & 3.60\% \\ Building b & Padua & 110 & 51 & 0 & 35 & 5 & 51 & 0 & 35 & 4 & 12.2 & 13.1 & \(-\)6.87\% \\ Building c & Vicenza & 127 & 30 & 7 & 40 & 8 & 25 & 0 & 43 & 4 & 16.8 & 16.1 & 4.35\% \\ Building d & Ravenna & 84 & 22 & 2 & 41 & 6 & 22 & 7 & 41 & 0 & 18.1 & 17.8 & 1.69\% \\ \hline \hline \end{tabular}
\end{table}
Table 11: Main geometrical characteristics and assessed heating energy consumption of four illustrative buildings.