# Hierarchical Modelling for CO\({}_{2}\) Variation Prediction for HVAC System Operation
## 6 Results and Discussion
### Transferability Assessment  
After proving its superior performance in predicting CO\({}_{2}\) variations in room00, the next stage assesses the transferability of the developed models by applying them to a smaller room, referred to as room01, which only fits two people. The FECOP models' results are obtained by training the models on the training set of room01. Both the HMCOVP and FECOP approaches are evaluated on the testing set of room01 using the **Thresh_MAE** metric. The evaluation criteria include the testing time per instance to infer the computational footprint of these methods. As for the HMCOVP, the models developed using room00's training data are applied to the testing data of room01 without fine-tuning any of its individual learners or ensemble learner. As such, the transferability of the developed models is assessed in different spatial settings. Table 5 summarises the results of the outlined process. In terms of predictive performance, the untuned HMCOVP outperforms its counterpart in every h&f combination. The HMCOVP models performed best with the h-15_f-15 and h-20_f-20 compared to other combinations. The h-15_f-15 combination performed best in terms of its **Thresh_MAE**, breaking the established trend of increasing **Thresh_MAE** with the increase in the prediction horizon. The h-20_f-20 experienced the least performance percentage gap in **Thresh_MAE** from room00 to room01. This observation means that the larger room's environment dynamics acquired through hierarchical modelling closely resemble those of the smaller room in the bespoke combinations. As for smaller prediction horizons, it is expected that smaller rooms \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameter** & \multicolumn{3}{c}{**Thresh\_MAE**} & \multicolumn{3}{c}{**Training Time (min)**} \\ \hline
**Methodologies** & **HMCOVP** & **FECOP** & **1D-CNN** & **HMCOVP** & **FECOP** & **1D-CNN** \\ \hline h-5\_f-5 & **10.14** & 40.89 & 2331.11 & 229.69 & 2.1 & 36.5 \\ \hline h-10\_f-10 & **14.48** & 52.52 & 8969.98 & 360.34 & 2.275 & 22.62 \\ \hline h-15\_f-15 & **19.37** & 66.83 & 9201.81 & 716.54 & 2.83 & 19.16 \\ \hline h-20\_f-20 & 27.74 & 77.21 & 10,128.83 & 381.78 & 3.62 & 17.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: HMCOVP vs. FECOP vs. 1D-CNN. would exhibit different variations. In fact, changes in the small room's environment, such as the existence of occupants, can momentarily affect the CO\({}_{2}\) concentrations as opposed to the more spacious rooms. Lastly, the differences in the capacities of both rooms result in changes in the ranges of activity level-related features; thus, affecting the HMCOVP models' accuracy. Consistent with the previous analysis, the FECOP approach is a less time and resource-intensive approach, manifested by its lower per-instance testing time. A 6-7\(\times\) speedup is obtained by the FECOP approach; however, at the expense of its underwhelming prediction performance. The speedup benefit is blurred when the individual learners' are parallelised. The differences in feature scales between the two rooms require incorporating some of these missing characteristics into the developed HMCOVP model. Thanks to the hierarchical structure of the HMCOVP, the induction of this novel information can be realized on the level of individual and ensemble learners. As a result, the next step can include one of these scenarios. The first scenario re-tunes the individual CNN models by freezing some layers and training others. The second scenario replaces the old ensemble trained on room00 training data with a newer one trained using room01's training data. While both scenarios are viable, choosing one of them depends on the obtained results and the nature of the data. The results have shown that the greatest performance divergence occurs in the ensemble learning phase as the individual learners almost produce the same accuracy results in both rooms. This gap can be surmised by the differences in e2s values and their effect on the future CO\({}_{2}\) variations.