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90_Conclusion.tex

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+\section{Conclusion}~\label{sec:conclusion}
+
+The aim of this project was to analyse the performance of \acrshort{gp} based
+controllers for use in longer lasting implementations, where differences in
+building behaviour become important compared to the initially available data.
+
+{\color{red}
+First, the performance of a classical \acrshort{gp} model trained on 5 days
+worth of experimental data was analysed. This model turned out to be unable to
+correctly extrapolate building behaviour as the weather changed throughout the
+year.
+}
+
+First, the performance of a classical \acrshort{gp} model trained on five days
+worth of experimental data was analysed. Initially, this model performed very
+well both in one step ahead prediction and multi-step ahead simulation over new,
+unseen, data. With the change in weather, however, the model shifted  
+
+Several \acrshort{svgp} implementations were then analysed. They turned out to
+provide important benefits over the classical models, such as the ability to
+easily scale when new data is being added and the much reduced computational
+effort required. They do however present some downsides, namely increasing the
+number of hyperparameters by having to choose the number of inducing locations,
+as well as performing worse than then classical \acrshort{gp} implementation
+given the same amount of data.
+
+%Finally, the possible improvements to the current implementations have been
+%addressed, noting that classical \acrshort{gp} implementations could also be
+%adapted to the \textit{learning control} paradigm, even if their implementation
+%could turn out to be much more involved and more computationally expensive than
+%the \acrshort{svgp} alternative.
+
+
+\subsection{Further Research}~\label{sec:further_research}
+
+Section~\ref{sec:results} has presented and compared the results of a full-year
+simulation for a classical \acrshort{gp} model, as well as a few incarnations of
+\acrshort{svgp} models. The results show that the \acrshort{svgp} have much
+better performance, mainly due to the possibility of updating the model
+throughout the year. The \acrshort{svgp} models also present a computational
+cost advantage both in training and in evaluation, due to several approximations
+shown in Section~\ref{sec:gaussian_processes}.
+
+Focusing on the \acrlong{gp} models, there could be several ways of improving
+its performance, as noted previously: a more varied identification dataset and
+smart update of a fixed-size data dictionary according to information gain,
+could mitigate the present problems.
+
+Using a Sparse \acrshort{gp} without replacing the maximum log likelihood
+with the \acrshort{elbo} could improve performance of the \acrshort{gp} model at
+the expense of training time.
+
+An additional change that could be made is inclusion of the most amount of prior
+information possible through setting a more refined kernel, as well as adding
+prior information on all the model hyperparameters when available. This approach
+however goes against the `spirit' of black-box approaches, since significant
+insight into the physics of the plant is required in order to properly model and
+implement this information.
+
+On the \acrshort{svgp} side, several changes could also be proposed, which were
+not properly addressed in this work. First, the size of the inducing dataset was
+chosen experimentally until it was found to accurately reproduce the manually
+collected experimental data. In order to better use the available computational
+resources, this value could be found programmatically in a way to minimize
+evaluation time, while still providing good performance. Another possibility is
+the periodic re-evaluation of this value when new data comes in, since as more
+and more data is collected the model becomes more complex, and in general more
+inducing locations could be necessary to properly reproduce the training data.
+
+Finally, none of the presented controllers take into account occupancy rates or
+adapt to possible changes in the real building, such as adding or removing
+furniture, deteriorating insulation and so on. The presented update methods only
+deals with adding information on behaviour in different state space regions, i.e
+\textit{learning}. Additionally, their ability to \textit{adapt} to changes in
+the actual plant's behaviour should be further addressed.
+
+\section*{Acknowledgements}
+
+I would like to thank Manuel Koch for the great help provided during the course
+of the project starting from the basics on CARNOT modelling, to helping me
+better compare the performance of different controllers, as well as Prof.\ Colin
+Jones, whose insights were always very guiding, while still allowing me to
+discover everything on my own.
+
+\clearpage