## 3 Results
### Impact of Data Quality on ANN Performance  
An observation of the following graphs (Figure 7) highlights the excellent fit of the network trained with the full training data (ANN 1). The thick grey line on all graphs represents the ground truth--that is, the actual temperature development on the non-exposed face of the wall through time. The dotted line representing the predictions made by ANN 1 coincides almost entirely with the ground truth line. The above observation is very well recorded and reinforced by the metric results. The indices used to evaluate the performance of the fully trained network (ANN 1) when tested against the ground truth are summarised in Table 8. The algorithm manages to predict the final temperature with a maximum error of 2.55 \({}^{\circ}\)C, which translates to 2.2% (test on Wall Assembly 3) of the scale of the overall developed temperatures throughout the analysis. The good fit is evident not only on the final temperature prediction but throughout the process, where the maximum error appears to be 3.0 \({}^{\circ}\)C. The overall agreement between the trained algorithm and the ground truth is demonstrated by the Mean Absolute Error, which on average is 0.73 \({}^{\circ}\)C (or a 2.62% difference between the observed values and their mean). An average of 0.9992 coefficient of determination provides robust evidence of the agreement between the observed and predicted data. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Metric** & **Reference** & **Formula 1** & **Perfect Score** \\ \hline Absolute maximum error & AME & AME = max\(\langle\)1 \(Q_{i}-\hat{Q}_{i}\) 1\(\rangle\) & 0.0 \\ Mean absolute error & MAE & MAE = \(\frac{1}{\mu}\sum\limits_{i=1}^{n}\left|Q_{i}-\hat{Q}_{i}\right|\) & 0.0 \\ Relative absolute error & RAE & RAE = \(\frac{\sum_{i=1}^{n}\left|Q_{i}-\hat{Q}_{i}\right|}{\sum_{i=1}^{n}\left|Q_{i}- \hat{Q}_{i}\right|}\) & 0.0 \\ Peak difference & PDIFF & PDIFF = max\((Q_{i})\) \(-\) max\((\hat{Q}_{i})\) & 0.0 \\ Per cent error in peak & PEP & PEP = \(\frac{\max(Q_{i})\)\(-\) max\((\hat{Q}_{i})}{\max(\hat{Q}_{i})}\times 100\) & 0.0 \\ Root mean squared error & RMSE & RMSE = \(\sqrt{\frac{\sum_{i=1}^{n}\left(Q_{i}-\hat{Q}_{i}\right)}{n}}\) & 0.0 \\ Coefficient of determination & R2 & R2 = \(\left[\frac{\sum_{i=0}^{n}\left(Q_{i}-\hat{Q}\right)\left(\hat{Q}-\hat{Q}\right)} {\sqrt{\sum_{i=1}^{n}\left(Q_{i}-\hat{Q}\right)^{2}}}\right]^{2}\) & 1.0 \\ \hline \hline \end{tabular}  
* Nomenclature of the above formulas: n = number of data points; \(Q_{i}\) = observed value; \(\hat{Q}_{i}\) = ANN value prediction; \(\overline{Q}\) = mean of the observed data points; \(\hat{Q}\) = mean of the values predicted by the ANN.  
\end{table} 
Table 7: Metrics used for the evaluations of the performance of the ANN. The training data offered to ANN 2 was deprived of any middle values of insulation thickness (removed observations incorporating 50 mm insulation externally or internally). The graphical representation of the network's predictions reveals that the algorithm, despite the reduced data, still captures the \"essence\" of the physical phenomenon and follows the route of the ground truth curve. Clearly, a perfect fit is not achieved; the prediction lines generally run close but parallel to the ground truth curve. Wall Assembly 4 (WA4) is an exception, where the two lines cross at timestamp 15,300 s; the temperature predictions decline from there onwards. Figure 7: Graphical representation of the predictive performance of the 4 ANN models (same algorithm, varying quality of input data). The above is reflected in the performance indices in Table 9. The predictions of the final temperature are generally within \(-\)0.30 \({}^{\circ}\)C and 6.76 \({}^{\circ}\)C (\(-\)0.24% and 6.27% of the observed values, respectively) of the actual values. As observed graphically, the final prediction error for WA4 lies at 11.85 \({}^{\circ}\)C (10.37% error compared to the actual temperature value), slightly beyond the range seen on the other tests.