# Prediction of Building's Thermal Performance Using LSTM and MLP Neural Networks
## 3 Results and Discussion
### Temperatures Analysis
On the contrary, the structure that produces the highest average error is the 6-lag structure (CV(RMSE) = 2.06%). In this case, and similarly to LSTM models, there is no direct relation between average error and variability in the results. In addition, as can be seen in the first row of Figure 5b (and the first row of Figure 5a), none of the models are able to replicate the peaks of the indoor temperatures at the weekend. Nevertheless, as shown in Table 3, the models do adjust the data trend efficiently. On the other hand, in sample 2 (second row of Figure 5b), as in LSTM models, the average errors obtained are higher than those of sample 1 (see Table 3). In this case, the architecture that yielded the lowest average error is the 12-lags architecture (CV(RMSE) = 1.90%). Additionally, it is also the architecture that presents the smallest variability among its results. With this sample, the introduction of time lags did provide valuable information because, as shown in Table 3, the best model structures are those with 12 and 24 lags. However, the lag structure that presents the highest average error was 6-lag structure (CV(RMSE) = 2.28%), slightly worse than the average error  
Figure 5: Results of the temperatures predictions in sample 1 (upper side) and sample 2 (bottom side) considering the different structures of time lags. Each architecture is represented by the prediction curve with the lowest error among the 10 repetitions: (**a**) LSTM models; (**b**) MLP models. of the model without any lag. This means that, although the introduction of time lags provides useful information, the basic model (regardless of thermal inertia) already provides good results. Regarding the results of the indoor temperatures of the building, it can be observed that, on the one hand, there are less differences between the performance of the models in the different samples than in the case of the thermal demand. Moreover, in comparison with the thermal demand results, the different errors obtained for each of the architectures analyzed during the repetitions are lower and less variable. This demonstrates that indoor temperature values are more constant throughout a year (always around the set point temperature of the building). On the other hand, there are differences between LSTM and MLP models (see Table 3). With LSTM models the thermal inertia is less significant than in the case of thermal demand. In the two samples analyzed the best model was the one with a single time lag. In contrast, with MLP models the thermal inertia is more significant than in the analysis in the previous section. In both samples, the best model structures were a 24-lag structure for sample 1 and a 12-lag structure for sample 2; they use information from a higher number of past hours. In this case, MLP models show better performance in both the best and the worst case. In addition, even with less variability in general concerning indoor temperature predictions, MLP models again produced the lowest standard deviations. Finally, as in the case of thermal demand predictions, models without time lags do not produce the lowest average error in any of the analyses presented. This indicates that the thermal inertia is also significant in the case of indoor temperatures predictions.