Updated README file

.github/workflows/compile.yml

@@ -6,7 +6,6 @@ name: CI
 on:
   # Triggers the workflow on push or pull request events but only for the master branch
   push:
-    branches: [ master ]
     tags:
       - 'v*.*.*'
   pull_request:
@@ -31,12 +30,18 @@ jobs:
       - name: Compile LaTeX document
         uses: xu-cheng/latex-action@v2
         with:
-          root_file: main.tex          
+          root_file: |
+            thesis.tex
+            slides_clean.tex
+            slides_notes.tex
           
       - name: Release
         uses: softprops/action-gh-release@v1
         if: startsWith(github.ref, 'refs/tags/')
         with:
-          files: main.pdf
+          files: |
+            thesis.pdf
+            slides_clean.pdf
+            slides_notes.pdf
         env:
           GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}

.gitignore

@@ -0,0 +1,291 @@
+## Core latex/pdflatex auxiliary files:
+*.aux
+*.lof
+*.log
+*.lot
+*.fls
+*.out
+*.toc
+*.fmt
+*.fot
+*.cb
+*.cb2
+.*.lb
+
+## Intermediate documents:
+*.dvi
+*.xdv
+*-converted-to.*
+# these rules might exclude image files for figures etc.
+# *.ps
+# *.eps
+thesis.pdf
+slides_clean.pdf
+slides_notes.pdf
+*Master_report*.pdf
+
+## Generated if empty string is given at "Please type another file name for output:"
+.pdf
+
+## Bibliography auxiliary files (bibtex/biblatex/biber):
+*.bbl
+*.bcf
+*.blg
+*-blx.aux
+*-blx.bib
+*.run.xml
+
+## Build tool auxiliary files:
+*.fdb_latexmk
+*.synctex
+*.synctex(busy)
+*.synctex.gz
+*.synctex.gz(busy)
+*.pdfsync
+
+## Build tool directories for auxiliary files
+# latexrun
+latex.out/
+
+## Auxiliary and intermediate files from other packages:
+# algorithms
+*.alg
+*.loa
+
+# achemso
+acs-*.bib
+
+# amsthm
+*.thm
+
+# beamer
+*.nav
+*.pre
+*.snm
+*.vrb
+
+# changes
+*.soc
+
+# comment
+*.cut
+
+# cprotect
+*.cpt
+
+# elsarticle (documentclass of Elsevier journals)
+*.spl
+
+# endnotes
+*.ent
+
+# fixme
+*.lox
+
+# feynmf/feynmp
+*.mf
+*.mp
+*.t[1-9]
+*.t[1-9][0-9]
+*.tfm
+
+#(r)(e)ledmac/(r)(e)ledpar
+*.end
+*.?end
+*.[1-9]
+*.[1-9][0-9]
+*.[1-9][0-9][0-9]
+*.[1-9]R
+*.[1-9][0-9]R
+*.[1-9][0-9][0-9]R
+*.eledsec[1-9]
+*.eledsec[1-9]R
+*.eledsec[1-9][0-9]
+*.eledsec[1-9][0-9]R
+*.eledsec[1-9][0-9][0-9]
+*.eledsec[1-9][0-9][0-9]R
+
+# glossaries
+*.acn
+*.acr
+*.glg
+*.glo
+*.gls
+*.glsdefs
+*.lzo
+*.lzs
+
+# uncomment this for glossaries-extra (will ignore makeindex's style files!)
+# *.ist
+
+# gnuplottex
+*-gnuplottex-*
+
+# gregoriotex
+*.gaux
+*.glog
+*.gtex
+
+# htlatex
+*.4ct
+*.4tc
+*.idv
+*.lg
+*.trc
+*.xref
+
+# hyperref
+*.brf
+
+# knitr
+*-concordance.tex
+# TODO Uncomment the next line if you use knitr and want to ignore its generated tikz files
+# *.tikz
+*-tikzDictionary
+
+# listings
+*.lol
+
+# luatexja-ruby
+*.ltjruby
+
+# makeidx
+*.idx
+*.ilg
+*.ind
+
+# minitoc
+*.maf
+*.mlf
+*.mlt
+*.mtc[0-9]*
+*.slf[0-9]*
+*.slt[0-9]*
+*.stc[0-9]*
+
+# minted
+_minted*
+*.pyg
+
+# morewrites
+*.mw
+
+# newpax
+*.newpax
+
+# nomencl
+*.nlg
+*.nlo
+*.nls
+
+# pax
+*.pax
+
+# pdfpcnotes
+*.pdfpc
+
+# sagetex
+*.sagetex.sage
+*.sagetex.py
+*.sagetex.scmd
+
+# scrwfile
+*.wrt
+
+# sympy
+*.sout
+*.sympy
+sympy-plots-for-*.tex/
+
+# pdfcomment
+*.upa
+*.upb
+
+# pythontex
+*.pytxcode
+pythontex-files-*/
+
+# tcolorbox
+*.listing
+
+# thmtools
+*.loe
+
+# TikZ & PGF
+*.dpth
+*.md5
+*.auxlock
+
+# todonotes
+*.tdo
+
+# vhistory
+*.hst
+*.ver
+
+# easy-todo
+*.lod
+
+# xcolor
+*.xcp
+
+# xmpincl
+*.xmpi
+
+# xindy
+*.xdy
+
+# xypic precompiled matrices and outlines
+*.xyc
+*.xyd
+
+# endfloat
+*.ttt
+*.fff
+
+# Latexian
+TSWLatexianTemp*
+
+## Editors:
+# WinEdt
+*.bak
+*.sav
+
+# Texpad
+.texpadtmp
+
+# LyX
+*.lyx~
+
+# Kile
+*.backup
+
+# gummi
+.*.swp
+
+# KBibTeX
+*~[0-9]*
+
+# TeXnicCenter
+*.tps
+
+# auto folder when using emacs and auctex
+./auto/*
+*.el
+
+# expex forward references with \gathertags
+*-tags.tex
+
+# standalone packages
+*.sta
+
+# Makeindex log files
+*.lpz
+
+# xwatermark package
+*.xwm
+
+# REVTeX puts footnotes in the bibliography by default, unless the nofootinbib
+# option is specified. Footnotes are the stored in a file with suffix Notes.bib.
+# Uncomment the next line to have this generated file ignored.
+#*Notes.bib

.latexmkrc

@@ -1,4 +1,4 @@
 $pdf_mode = 1;
-@default_files = ('main.tex');
+@default_files = ('thesis.tex');
 
 $clean_ext = "bbl run.xml"

90_Further_Research.tex

@@ -1,42 +0,0 @@
-\section{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}, and their ability to \textit{adapt} to changes in the actual
-plant's behaviour should be further addressed.

EESD.cls

@@ -0,0 +1,217 @@
+% Mahmoud S. Shaqfa - EESD lab. - EPFL
+% Email: mahmoud.shaqfa@epfl.ch
+
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesClass{EESD}
+\LoadClass[aspectratio = 169, 11pt, xcolor={usenames,dvipsnames}]{beamer}
+% I used 16:9 aspect ratio of the slides; To get the default (4:3) remove the specifier above in-between the [aspectratio = 169] or simply change the value to 43
+% Other possible values are: 1610, 149, 54, 43 and 32.
+% \documentclass[aspectratio=1610]{beamer}
+% Sets aspect ratio to 16:10, and frame size to 160mm by 100mm.
+% 77
+% \documentclass[aspectratio=169]{beamer}
+% Sets aspect ratio to 16:9, and frame size to 160mm by 90mm.
+% \documentclass[aspectratio=149]{beamer}
+% Sets aspect ratio to 14:9, and frame size to 140mm by 90mm.
+% \documentclass[aspectratio=141]{beamer}
+% Sets aspect ratio to 1.41:1, and frame size to 148.5mm by 105mm.
+% \documentclass[aspectratio=54]{beamer}
+% Sets aspect ratio to 5:4, and frame size to 125mm by 100mm.
+% \documentclass[aspectratio=43]{beamer}
+% The default aspect ratio and frame size to 128mm by 96mm. You need not specify this option.
+% \documentclass[aspectratio=32]{beamer}
+% Sets aspect ratio to 3:2, and frame size to 135mm by 90mm.
+
+% ---- My Colors Specifiers ----
+\definecolor{mypink}{rgb}{0.97, 0.56, 0.65}
+\definecolor{myviolet}{rgb}{0.6, 0.4, 0.8}
+\definecolor{myblue}{rgb}{0.61, 0.77, 0.89}
+
+\definecolor{green1}{rgb}{0.00, 0.45, 0.47} % darker green
+\definecolor{green2}{rgb}{0.73, 0.88, 0.82} % light green
+
+\definecolor{violet1}{rgb}{0.59, 0.08, 0.39} % darker violet
+\definecolor{violet2}{rgb}{0.85, 0.78, 0.85} % light violet
+
+
+\definecolor{beamerfooter1}{rgb}{0.97, 0.64, 0.60}
+\definecolor{beamerfooter2}{rgb}{0.96, 0.46, 0.40}
+\definecolor{beamerfooter3}{rgb}{0.93, 0.19, 0.10}
+
+\setbeamercolor*{header color}{fg=white,bg=black}
+\setbeamercolor*{footer color1}{fg=black}%,bg=beamerfooter1} % pink
+\setbeamercolor*{footer color2}{fg=white}%,bg=beamerfooter2} % dark pink
+\setbeamercolor*{footer color3}{fg=white}%,bg=beamerfooter3} % dark red
+
+\setbeamertemplate{blocks}[rounded][shadow=true]
+
+\setbeamercolor{block body}{fg = black, bg = beamerfooter1}
+\setbeamercolor{block title}{fg=white, bg=beamerfooter2}
+
+\setbeamercolor{block body example}{fg = black, bg = green2}
+\setbeamercolor{block title example}{fg = white, bg = green1}
+
+\setbeamercolor{block body alerted}{fg = black, bg = violet2}
+\setbeamercolor{block title alerted}{fg=white, bg=violet1}
+
+\pgfdeclarehorizontalshading[beamerfooter1,beamerfooter2,beamerfooter3]
+    {beamer@frametitleshade}{\paperheight}{
+    color(0pt)=(beamerfooter3);
+    color(0.3333\paperwidth)=(beamerfooter2);
+    color(1.056\paperwidth)=(beamerfooter1)
+}
+
+\setbeamertemplate{frametitle}{\vspace{20pt}\color{beamerfooter3}\textbf\insertframetitle}
+
+% ---- Bibliography Specifiers ----
+\setbeamertemplate{bibliography item}[text] % Regular numbering (Formal)
+
+% ---- Itemize Specifier ----
+\setbeamertemplate{itemize items}[square]
+\setbeamertemplate{enumerate items}[square]
+
+% ---- Frame Title Specifier ----
+\addtobeamertemplate{frametitle}{}{\vspace{0pt}} % increase vspace between the title and text
+
+
+\newcommand{\rom}[1]{\uppercase\expandafter{\romannumeral #1\relax}} % Add Romans numbering
+
+\usecolortheme[named=beamerfooter3]{structure}
+\setbeamertemplate{headline}{}
+\setlength{\footnotesep}{0.05cm}
+
+% Table of contents size subsections and subsubsections
+\setbeamerfont{subsection in toc}{size=\scriptsize}
+\setbeamerfont{subsubsection in toc}{size=\scriptsize}
+
+% Table of contents (Enumeration shapes)
+\setbeamertemplate{section in toc}[square]
+\setbeamertemplate{subsection in toc}[square]
+\setbeamertemplate{subsubsection in toc}[square]
+
+\setbeamercovered{transparent} % Transparent Text When Use "Pauses"!
+\setbeamertemplate{navigation symbols}%{default}
+
+\logo{\centering\includegraphics[height=1.43cm]{logos169.pdf}\vspace{220pt}}
+
+\addtobeamertemplate{footnote}{}{\vspace{1.5ex}}
+
+% -------- Special frames ---------
+\newcommand{\coverpage}[1]{
+{
+    \setbeamertemplate{headline}{
+        \leavevmode
+          \hbox{
+            \begin{beamercolorbox}[wd=1.009\textwidth, ht=2.5ex, dp=1.125ex]{}
+            \end{beamercolorbox}
+          }
+        }
+\setbeamertemplate{footline}
+{
+    \leavevmode%
+    \setbox\beamer@tempbox=\hbox{%
+        \begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex, center]{footer color3}%
+            \usebeamerfont{author in head/foot}\hspace{2ex}\insertshortauthor
+        \end{beamercolorbox}%
+        \begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,center]{footer color2}%
+            % \usebeamerfont{title in head/foot}\insertshorttitle
+        \end{beamercolorbox}%
+        \begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,right]{footer color1}%
+            \usebeamerfont{title in head/foot}\insertshorttitle{}\hspace*{6em}~~~~~~~~\hspace*{2ex} 
+        \end{beamercolorbox}%
+        }%
+        \beamer@tempdim=\ht\beamer@tempbox%
+        \advance\beamer@tempdim by 4pt%
+        \begin{pgfpicture}{0pt}{0pt}{\paperwidth}{20pt}
+            \pgfpathrectangle{\pgfpointorigin}{\pgfpoint{\paperwidth}{\beamer@tempdim}}
+            \pgfusepath{clip}
+            \pgftext[left,base]{\pgfuseshading{beamer@frametitleshade}}
+        \end{pgfpicture}
+        \vskip-\beamer@tempdim%
+        \box\beamer@tempbox%    
+}%
+    \setbeamercolor{background canvas}{}
+    \begin{frame}[t, noframenumbering, allowframebreaks]{}
+        #1
+    \end{frame}
+}
+}
+
+% Define and customize the headline style of slides
+\setbeamertemplate{headline}{%
+\leavevmode%
+  \hbox{%
+    \begin{beamercolorbox}[wd=1.000\textwidth, ht=2.5ex, dp=1.125ex]{header color}%
+        \ifx\insertsubsection\empty % no subsection
+            {{~~}\insertsection}%
+        \else % subsection exists
+        \ifx\insertsubsubsection\empty % subsection but no subsubsection
+            {~\insertsection \textcolor{white}{$~~\bullet$} ~\S~\insertsubsection}%
+        \else % subsection and subsubsection exist
+            {~\insertsection \textcolor{white}{$~~\bullet$} ~\S~\insertsubsection \textcolor{white}{$~~\bullet$} ~\S~\insertsubsubsection}%
+        \fi
+        \fi
+    \end{beamercolorbox}%
+  }
+}
+
+\newcommand{\breakingframe}[1]{
+{
+
+    \setbeamertemplate{footline}
+{
+    \leavevmode%
+    \setbox\beamer@tempbox=\hbox{%
+        \begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex, center]{footer color3}%
+            \usebeamerfont{author in head/foot}\hspace{2ex}\insertshortauthor
+        \end{beamercolorbox}%
+        \begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,center]{footer color2}%
+            \usebeamerfont{title in head/foot}\insertshorttitle
+        \end{beamercolorbox}%
+        \begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,right]{footer color1}%
+            \usebeamerfont{date in head/foot}\insertshortdate{}\hspace*{6em}~~~~~~~~\hspace*{2ex} 
+        \end{beamercolorbox}%
+        }%
+        \beamer@tempdim=\ht\beamer@tempbox%
+        \advance\beamer@tempdim by 4pt%
+        \begin{pgfpicture}{0pt}{0pt}{\paperwidth}{20pt}
+            \pgfpathrectangle{\pgfpointorigin}{\pgfpoint{\paperwidth}{\beamer@tempdim}}
+            \pgfusepath{clip}
+            \pgftext[left,base]{\pgfuseshading{beamer@frametitleshade}}
+        \end{pgfpicture}
+        \vskip-\beamer@tempdim%
+        \box\beamer@tempbox%    
+}%
+
+    \setbeamercolor{background canvas}{bg=beamerfooter1}
+    \begin{frame}[t, noframenumbering, allowframebreaks]{}
+        #1
+    \end{frame}
+}
+}
+
+\setbeamertemplate{footline}
+{
+    \leavevmode%
+    \setbox\beamer@tempbox=\hbox{%
+        \begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex]{footer color3}%
+            \usebeamerfont{author in head/foot}\hspace{2ex}\insertshortauthor
+        \end{beamercolorbox}%
+        \begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,center]{footer color2}%
+            \usebeamerfont{title in head/foot}\insertshorttitle
+        \end{beamercolorbox}%
+        \begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,right]{footer color1}%
+            \usebeamerfont{date in head/foot}\insertshortdate{}\hspace*{2em}
+            \insertframenumber{} / \inserttotalframenumber\hspace*{2ex} 
+        \end{beamercolorbox}%
+        }%
+        \beamer@tempdim=\ht\beamer@tempbox%
+        \advance\beamer@tempdim by 4pt%
+        \begin{pgfpicture}{0pt}{0pt}{\paperwidth}{20pt}
+            \pgfpathrectangle{\pgfpointorigin}{\pgfpoint{\paperwidth}{\beamer@tempdim}}
+            \pgfusepath{clip}
+            \pgftext[left,base]{\pgfuseshading{beamer@frametitleshade}}
+        \end{pgfpicture}
+        \vskip-\beamer@tempdim%
+        \box\beamer@tempbox%    
+}%

README.md

@@ -0,0 +1,40 @@
+# Inter-seasonal GP MPC control for buildings
+
+## Report and Presentation slides
+
+This repository contains the code for the report and presentation slides for my
+Master Project 
+> *Inter-seasonal Performance of Gaussian Process-based 
+> Model Predictive Control of Buildings*
+
+which was done under the supervision of Prof. Colin Jones at the EPFL's
+[Automatic Control Laboratory](https://www.epfl.ch/labs/la/)
+
+The main folder structure is as follows: 
+
+```shell
+└── Thesis
+    ├── Images
+    ├── Plots
+    └── Sections
+```
+
+The `Images` and `Plots` folders contain the figures used in the thesis and are
+shared between the report and the presentation. The `Sections` folder contains
+the content of documents. 
+
+In order to compile the documents, the appropriate main file has to be chosen: 
+
+- `thesis.tex` compiles the project report
+- `slides_clean.tex` compiles the presentation slides, not including the notes
+- `slides_notes.tex` compiles the presentation slides, including the notes on
+  the right side of the screen.
+
+The resulting presentation pdf contains an embedded video file. It can be played
+back using a compatible pdf reader, such as okular or pympress.
+
+---
+
+The presentation is based on the
+[beamer template](https://www.overleaf.com/latex/templates/eesd-presentation-latex-template/sfqmhmqxhmjy)
+by Mahmoud Shaqfa.

Sections/10_Introduction.tex

@@ -17,12 +17,14 @@ design of these control schemes, as the results could vary greatly from one
 implementation to another.
 
 Gaussian Processes have been previously used to model building dynamics, but
-they are usually limited by a fixed computational budget. This limits the
+they are usually limited by a fixed computational
-approaches that can be taken for identification and update of said models.
+budget~\cite{jainLearningControlUsing2018,nghiemDatadrivenDemandResponse2017}.
-Learning \acrshort{gp} models have also been previously used in the context of
+This limits the approaches that can be taken for identification and update of
-autonomous racing cars \cite{kabzanLearningBasedModelPredictive2019}, but there
+said models.  Learning \acrfull{gp} models have also been previously used in
-the Sparse \acrshort{gp} model was built on top of a white-box model and only
+the context of autonomous racing cars
-responsible for fitting the unmodeled dynamics. 
+\cite{kabzanLearningBasedModelPredictive2019}, but there the Sparse
+\acrshort{gp} model was built on top of a white-box model and only responsible
+for fitting the unmodeled dynamics.
 
 \subsection{Previous Research}
 With the increase in computational power and availability of data  over time,
@@ -33,7 +35,7 @@ The idea of using Gaussian Processes as regression models for control of dynamic
 systems is not new, and has already been explored a number of times. A general
 description of their use, along with the necessary theory and some example
 implementations is given in~\cite{kocijanModellingControlDynamic2016}.
-In~\cite{pleweSupervisoryModelPredictive2020}, a \acrlong{gp} Model with a
+In~\cite{pleweSupervisoryModelPredictive2020}, a \acrshort{gp} Model with a
 \acrlong{rq} Kernel is used for temperature set point optimization.
 
 Gaussian Processes for building control have also been studied before in the
@@ -64,7 +66,7 @@ the original identified model goes further and further into the extrapolated
 regions.
 
 This project tries to combine the use of online learning control schemes with
-\acrlong{gp} Models through implementing \acrlong{svgp} Models. \acrshort{svgp}s
+\acrshort{gp} Models through implementing \acrfull{svgp} Models. \acrshort{svgp}s
 provide means of extending the use of \acrshort{gp}s to larger datasets, thus
 enabling the periodic re-training of the model to include all the historically
 available data.
@@ -79,7 +81,7 @@ multiple control schemes using both classical \acrshort{gp}s, as well as
 Section~\ref{sec:gaussian_processes} provides the mathematical background for
 understanding \acrshort{gp}s, as well as the definition in very broad strokes of
 \acrshort{svgp}s and their differences from the classical implementation of
-\acrlong{gp}es. This information is later used for comparing their performances
+\acrshort{gp}s. This information is later used for comparing their performances
 and outlining their respective pros and cons.
 
 Section~\ref{sec:CARNOT} goes into the details of the implementation of the

Sections/30_Gaussian_Processes_Background.tex

@@ -144,7 +144,7 @@ choices~\cite{kocijanModellingControlDynamic2016}:
 \subsubsection*{Squared Exponential Kernel}
 
 This kernel is used when the system to be modelled is assumed to be smooth and
-continuous. The basic version of the \acrshort{se} kernel has the following form:
+continuous. The basic version of the \acrfull{se} kernel has the following form:
 
 \begin{equation}
     k(\mathbf{x}, \mathbf{x'}) = \sigma^2 \exp{\left(- \frac{1}{2}\frac{\norm{\mathbf{x} -
@@ -182,7 +182,7 @@ value of the hyperparameters. This is the \acrfull{ard} property.
 
 The \acrfull{rq} Kernel can be interpreted as an infinite sum of \acrshort{se}
 kernels with different lengthscales. It has the same smooth behaviour as the
-\acrlong{se} Kernel, but can take into account the difference in function
+\acrshort{se} Kernel, but can take into account the difference in function
 behaviour for large scale vs small scale variations.
 
 \begin{equation}
@@ -207,11 +207,11 @@ without inquiring the penalty of inverting the covariance matrix. An overview
 and comparison of multiple methods is given
 at~\cite{liuUnderstandingComparingScalable2019}.
 
-For the scope of this project, the choice of using the \acrfull{svgp} models has
+For the scope of this project, the choice of using the \acrshort{svgp} models
-been made, since it provides a very good balance of scalability, capability,
+has been made, since it provides a very good balance of scalability, capability,
 robustness and controllability~\cite{liuUnderstandingComparingScalable2019}.
 
-The \acrlong{svgp} has been first introduced
+The \acrshort{svgp} has been first introduced
 by~\textcite{hensmanGaussianProcessesBig2013} as a way to scale the use of
 \acrshort{gp}s to large datasets. A detailed explanation on the mathematics of
 \acrshort{svgp}s and reasoning behind it is given
@@ -264,7 +264,7 @@ In order to solve this problem, the log likelihood equation
 classical \acrshort{gp} is replaced with an approximate value, that is
 computationally tractable on larger sets of data.
 
-The following derivation of the \acrshort{elbo} is based on the one presented
+The following derivation of the \acrfull{elbo} is based on the one presented
 in~\cite{yangUnderstandingVariationalLower}.
 
 Assume $X$ to be the observations, and $Z$ the set parameters of the
@@ -300,7 +300,7 @@ divergence, which for variational inference takes the following form:
 \end{equation}
 \vspace{5pt}
 
-where L is the \acrfull{elbo}. Rearranging this equation we get: 
+where L is the \acrshort{elbo}. Rearranging this equation we get:
 
 \begin{equation}
     L = \log{\left(p(X)\right)} - KL\left[q(Z)||p(Z|X)\right] 
@@ -312,13 +312,13 @@ lower bound of the log probability of observations.
 \subsection{Gaussian Process Models for Dynamical
 Systems}\label{sec:gp_dynamical_system}
 
-In the context of Dynamical Systems Identification and Control, Gaussian
+In the context of Dynamical Systems Identification and Control, \acrshort{gp}s
-Processes are used to represent different model structures, ranging from state
+are used to represent different model structures, ranging from state
-space and \acrshort{nfir} structures, to the more complex \acrshort{narx},
+space and \acrfull{nfir} structures, to the more complex \acrfull{narx},
-\acrshort{noe} and \acrshort{narmax}. 
+\acrfull{noe} and \acrfull{narmax}.
 
 
-The general form of an \acrfull{narx} model is as follows:
+The general form of an \acrshort{narx} model is as follows:
 
 \begin{equation}
     \hat{y}(k) =

Sections/40_CARNOT_model.tex

@@ -378,7 +378,7 @@ The unit has a typical \acrlong{eer} (\acrshort{eer}, cooling efficiency) of 4.9
 maximum cooling capacity of 64.2 kW. 
 
 One particularity of this \acrshort{hvac} unit is that during summer, only one
-of the two compressors are running. This results in a higher \acrlong{eer}, in
+of the two compressors are running. This results in a higher \acrshort{eer}, in
 the cases where the full cooling capacity is not required.
 
 \subsubsection*{Ventilation}
@@ -504,7 +504,7 @@ it will oscillate between using one or two compressors. Lastly, it is possible
 to notice that the \acrshort{hvac} is not turned on during the night, with the
 exception of the external fan, which continues running.
 
-\subsubsection{The CARNOT WDB weather data format}\label{sec:CARNOT_WDB}
+\subsubsection{The CARNOT Weather Data Bus format}\label{sec:CARNOT_WDB}
 
 For a correct simulation of the building behaviour, CARNOT requires not only the
 detailed definition of the building blocks/nodes, but also a very detailed set
@@ -514,7 +514,7 @@ sun's position throughout the simulation (zenith and azimuth angles), the
 as well as information on the ambient temperature, humidity, precipitation,
 pressure, wind speed and direction, etc.  A detailed overview of each
 measurement necessary for a simulation is given in the CARNOT user
-manual~\cite{CARNOTManual}.
+manual~\cite{CARNOTManual}. This data structure is known as the \acrfull{wdb}.
 
 In order to compare the CARNOT model's performance to that of the real \pdome,
 it is necessary to simulate the CARNOT model under the same set of conditions as
@@ -532,17 +532,19 @@ are computed using the Python pvlib
 library~\cite{f.holmgrenPvlibPythonPython2018}.
 
 As opposed to the solar angles, which can be computed exactly from the available
-information, the Solar Radiation Components (DHI and DNI) have to be estimated
+information, the Solar Radiation Components (\acrshort{dhi} and \acrshort{dni})
-from the available measurements of GHI, zenith angles (Z) and datetime
+have to be estimated from the available measurements of \acrfull{ghi}, zenith
-information.  \textcite{erbsEstimationDiffuseRadiation1982} present an empirical
+angles (Z) and datetime information.
-relationship between GHI and the diffuse fraction DF and the ratio of GHI to
+\textcite{erbsEstimationDiffuseRadiation1982} present an empirical relationship
-extraterrestrial irradiance $K_t$, known as the Erbs model. The DF is then used
+between \acrshort{ghi} and the \acrfull{df} and the ratio of \acrshort{ghi} to
-to compute DHI and DNI as follows:
+extraterrestrial irradiance $K_t$, known as the Erbs model.  The \acrshort{df}
+is then used to compute \acrshort{dhi} and \acrshort{dni} as follows:
 
 \begin{equation}
     \begin{aligned}
-        \text{DHI} &= \text{DF} \times \text{GHI} \\
+        \text{\acrshort{dhi}} &= \text{DF} \times \text{\acrshort{ghi}} \\
-        \text{DNI} &= \frac{\text{GHI} - \text{DHI}}{\cos{\text{Z}}}
+        \text{\acrshort{dni}} &= \frac{\text{\acrshort{ghi}} -
+        \text{\acrshort{dhi}}}{\cos{\text{Z}}}
     \end{aligned}
 \end{equation}
 

Sections/50_Choice_of_Hyperparameters.tex

@@ -19,7 +19,7 @@ consuming computations in the case of larger number of regressors and more
 complex kernel functions.
 
 As described in Section~\ref{sec:gp_dynamical_system}, for the purpose of this
-project, the \acrlong{gp} model will be trained using the \acrshort{narx}
+project, the \acrshort{gp} model will be trained using the \acrshort{narx}
 structure. This already presents an important choice in the selection of
 regressors and their respective autoregressive lags.
 
@@ -185,7 +185,7 @@ $l_u = 1$ and $l_y = 3$ with $l_w$ taking the values of either 1, 2 or 3,
 depending on the results of further analysis.
 
 
-As for the case of the \acrlong{svgp}, the results for the classical
+As for the case of the \acrshort{svgp}, the results for the classical
 \acrshort{gp} (cf. Table~\ref{tab:GP_hyperparameters}) are not necessarily
 representative of the relationships between the regressors of the
 \acrshort{svgp} model, due to the fact that the dataset used for training is
@@ -259,8 +259,8 @@ This performance metric is very useful when training a model whose goal is
 solely to minimize the difference between the measured values, and the ones
 predicted by the model.
 
-A variant of the \acrshort{mse} is the \acrfull{smse}, which normalizes the
+A variant of the \acrfull{mse} is the \acrfull{smse}, which normalizes the
-\acrlong{mse} by the variance of the output values of the validation dataset.
+\acrshort{mse} by the variance of the output values of the validation dataset.
 
 \begin{equation}\label{eq:smse}
     \text{SMSE} = \frac{1}{N}\frac{\sum_{i=1}^N \left(y_i -
@@ -403,7 +403,7 @@ the discrepancies.
 \subsubsection{Conventional Gaussian Process}
 
 The simulation performance of the three lag combinations chosen for the
-classical \acrlong{gp} models has been analyzed, with the results presented in
+classical \acrshort{gp} models has been analyzed, with the results presented in
 Figures~\ref{fig:GP_113_multistep_validation},~\ref{fig:GP_213_multistep_validation}
 and~\ref{fig:GP_313_multistep_validation}. For reference, the one-step ahead
 predictions for the training and test datasets are presented in

Sections/60_The_MPC_Problem.tex

@@ -41,7 +41,7 @@ buildings based on the rolling 48h average outside temperature.
 
 \begin{figure}[ht]
     \centering
-    \includegraphics[width = \textwidth]{Images/sia_180_2014.png}
+    \includegraphics[width = \textwidth]{Images/sia_180_2014_en.png}
     \caption{The SIA 180:2014 norm for residential building
     temperatures~\cite{sia180:2014ProtectionThermiqueProtection2014}}
     \label{fig:sia_temperature_norm}

Sections/70_Implementation.tex

@@ -48,7 +48,7 @@ the correct amount of data for the weather predictions and to properly generate
 the optimization problem, the discrete/continuous transition and vice-versa
 happens on the Simulink side. This simplifies the adjustment of the sampling
 time, with the downside of harder inclusion of meta-data such as hour of the
-day, day of the week, etc.\ in the \acrlong{gp} Model.
+day, day of the week, etc.\ in the \acrshort{gp} Model.
 
 The weather prediction is done using the information present in the CARNOT
 \acrshort{wdb} object. Since the sampling time and control horizon of the
@@ -66,13 +66,13 @@ evaluating a \acrshort{gp} has an algorithmic complexity of $\mathcal{O}(n^3)$.
 This means that naive implementations can get too expensive in terms of
 computation time very quickly.
 
-In order to have as smallest of a bottleneck as possible when dealing with
+In order to have as smallest of a bottleneck as possible when dealing with the
-\acrshort{gp}s, a very fast implementation of \acrlong{gp} Models was used, in
+required algebraic operations, a very fast implementation of \acrshort{gp}
-the form of GPflow~\cite{matthewsGPflowGaussianProcess2017}. It is based on
+Models was used, in the form of GPflow~\cite{matthewsGPflowGaussianProcess2017}.
-TensorFlow~\cite{tensorflow2015-whitepaper}, which has very efficient
+It is based on TensorFlow~\cite{tensorflow2015-whitepaper}, which has very
-implementation of all the necessary Linear Algebra operations. Another benefit
+efficient implementation of all the necessary Linear Algebra operations. Another
-of this implementation is the very simple use of any additional computational
+benefit of this implementation is the very simple use of any additional
-resources, such as a GPU, TPU, etc.
+computational resources, such as a GPU, TPU, etc.
 
 \subsubsection{Classical Gaussian Process training}
 
@@ -158,7 +158,7 @@ Let $w_l$, $u_l$, and $y_l$ be the lengths of the state vector components
 $\mathbf{w}$, $\mathbf{u}$, $\mathbf{y}$ (cf. Equation~\ref{eq:components}).
 Also, let X be the matrix of all the system states over the optimization horizon
 and W be the matrix of the predicted disturbances for all the future steps. The
-original \acrlong{ocp} can be rewritten using index notation as:
+original \acrshort{ocp} can be rewritten using index notation as:
 
 \begin{subequations}\label{eq:sparse_optimal_control_problem}
     \begin{align}

Sections/80_Results.tex

@@ -7,7 +7,7 @@ analyzed in this Section have used a sampling time of 15 minutes and a control
 horizon of 8 steps.
 
 Section~\ref{sec:GP_results} analyzes the results of a conventional
-\acrlong{gp} Model trained on the first five days of gathered data. The model
+\acrshort{gp} Model trained on the first five days of gathered data. The model
 is then used for the rest of the year, with the goal of tracking the defined
 reference temperature.
 
@@ -131,7 +131,7 @@ performance, but are more complex in implementation.
 
 \subsection{Sparse and Variational Gaussian Process}\label{sec:SVGP_results}
 
-The \acrlong{svgp} models are setup in a similar way as described before. The
+The \acrshort{svgp} models are setup in a similar way as described before. The
 model is first identified using 5 days worth of experimental data collected
 using a \acrshort{pi} controller and a random disturbance signal. The difference
 lies in the fact than the \acrshort{svgp} model gets re-identified every night
@@ -143,7 +143,7 @@ setup performs much better than the initial one. The only large deviations from
 the reference temperature are due to cold weather, when the \acrshort{hvac}'s
 limited heat capacity is unable to maintain the proper temperature.
 Additionnaly, the \acrshort{svgp} controller takes around 250 - 300ms of
-computation time for each simulation time, decreasing the computational cost of
+computation time for each simulation step, decreasing the computational cost of
 the original \acrshort{gp} by a factor of six.
 
 
@@ -293,7 +293,7 @@ As seen in Figure~\ref{fig:SVGP_evol_importance}, the variance of the
 signifies the increase in confidence of the model. The hyperparameters
 corresponding to the exogenous inputs --- $w1,1$ and $w1,2$ --- become generally
 less important for future predictions over the course of the year, with the
-importance of $w1,1$, the \acrlong{ghi}, climbing back up over the last, colder
+importance of $w1,1$, the \acrshort{ghi}, climbing back up over the last, colder
 months. This might be due to the fact that during the colder months, the
 \acrshort{ghi} is the only way for the exogenous inputs to \textit{provide}
 additional heat to the system.
@@ -361,7 +361,7 @@ simulation data (cf. Figures~\ref{fig:SVGP_96pts_fullyear_simulation}
 and~\ref{fig:SVGP_96pts_abserr}) it is very notable that the model performs
 almost identically to the one identified in the previous sections. This
 highlights one of the practical benefits of the \acrshort{svgp} implementations
-compared to the classical \acrlong{gp} -- it is possible to start with a rougher
+compared to the classical \acrshort{gp} -- it is possible to start with a rougher
 controller trained on less data and refine it over time, reducing the need for
 cumbersome and potentially costly initial experiments for gathering data.
 
@@ -473,7 +473,7 @@ models can be deployed with less explicit identification data, but they will
 continue to improve over the course of the year, as the building passes through
 different regions of the state space and more data is collected.
 
-However, these results do not discredit the use of \acrlong{gp} for employment
+However, these results do not discredit the use of \acrshort{gp} for employment
 in a multi-seasonal situation. As shown before, given the same amount of data
 and ignoring the computational cost, they perform better than the alternative
 \acrshort{svgp} models. The bad initial performance could be mitigated by

Sections/90_Conclusion.tex

@@ -62,7 +62,7 @@ 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
+Focusing on the \acrshort{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.

Sections/slides_content.tex

@@ -0,0 +1,676 @@
+{
+\coverpage{
+\titlepage{~}
+% To add additional text to the title components 
+{\newline \small \textit{Supervisor}: Prof. Colin Jones \quad \textit{Assistant}: Manuel Koch \quad
+\textit{Expert}: Bratislav Svetozarevic}
+\note[item]{Introduction, welcome}
+\note[item]{Present yourself and the thesis subject}
+\note[item]{Analysis of GP models performance for longer lasting simulations, in
+this case a full year}
+\note[item]{Discussion of the shortcomngs of classical GP approaches for these
+longer experiments and possible solutions}
+}
+}
+
+\setbeamertemplate{logo}{} % To override the logo from the other slides and delete it completely
+
+
+% Use smart division for the TOC
+\begin{frame}{Outlines}
+\begin{multicols}{2}
+\tableofcontents
+\end{multicols}
+\note[item]{The main work consists of two parts: the CARNOT building model serving as
+a plant for the simulation, and the definition and analysis of different GP/SVGP
+based control schemes}
+\note[item]{Starting with a short introduction where the motivation for these new
+approaches is presented, followed by the basic ideas of GP models}
+\end{frame}
+
+% -----------------------Introduction
+\section{Introduction}
+
+\breakingframe{
+\begin{textblock*}{3cm}[0.5,0.5](0.5\textwidth,  0.5\textheight)
+\Huge\textbf{\textcolor{black}{Introduction}}
+\end{textblock*}
+}
+
+
+\subsection{Residential buildings}
+
+\begin{frame}[t]{Residential buildings energy usage}
+    \begin{itemize}
+        \item Residential buildings represent more than 25\% of total energy
+            consumed in the EU \vspace{10pt} \pause
+        \item Average of 200-300 kWh/year/m$^{2}$ \vspace{10pt} \pause
+        \item Around 68\% of energy used for heating \vspace{10pt}
+    \end{itemize}
+
+    \note[item]{Residential buildings are a significant part of total energy
+    consumption in the EU}
+    \note[item]{Most of that energy is used for heating and ventilation of
+    buildings}
+    \note[item]{Additionally, there are increasing energy efficiency demands on
+    new and existing buildings}
+    \note[item]{Further improvements can be made by including already existing
+    buildings into "smart grids"}
+\end{frame}
+
+\begin{frame}
+    \frametitle{Limited information available}
+    \begin{block}{Existing infrastructure}
+    Most existing buildings already have in place Heating and Ventilation
+    Systems:\pause
+    \vspace{10pt}
+    \begin{itemize}
+        \item Limits the amount of available information \vspace{10pt} \pause
+        \item Restricts the actionable signals to those provided by the existing
+            HVAC \vspace{10pt}
+    \end{itemize}
+    \end{block}
+    \pause
+    \begin{block}{Weather forecast}
+    Predictions of future disturbance values for the MPC also impose
+    restrictions on usable data.
+    \end{block}
+    \note[item]{Polydome only has two temperature measurements}
+    \note[item]{Existing data lacks information on air humidity}
+    \note[item]{Existing data lacks information on occupancy\vspace{10pt}}
+    \note[item]{The only input for the Polydome's HVAC is the setpoint
+    temperature, thus only indirectly controlling the heat input\vspace{10pt}}
+    \note[item]{Weather predictions are restricted to outside temperature and
+    GHI}
+    \note[item]{This makes the use of other disturbances, such as humidity,
+    wind speed and direction, DNI, DHI inaccessible}
+\end{frame}
+
+\subsection{Black box models}
+
+\begin{frame}
+    \frametitle{Black-box models}
+    Data-driven models provide several practical benefits over first-principle
+    models:
+    \vspace{10pt}
+    \begin{itemize}
+        \item Foregoes complex and potentially expensive physical modelling \vspace{10pt} \pause
+        \item Same data-driven model structure could be applied to other
+            situations with less effort \vspace{10pt} \pause
+        \item Unknown/complex plant elements, such as HVAC behaviour, unknown
+            material properties , occupancy levels are much easier to include\vspace{10pt} \pause
+    \end{itemize}
+    \note[item]{In this context it would be very useful to be able to use
+    data-driven models as they provide several benetifs over white-box
+approaches:}
+    \note[item]{They forego the complex physical modelling step}
+    \note[item]{Applying a control scheme using a white-box model requires a
+    complete identification step, whereas for data-driven models only the
+hyperparameters have to be tuned}
+    \note[item]{For buildings where not all information is readily available,
+    white-box models can prove infeasible (eg. The Polydome building :D)}
+\end{frame}
+
+
+% ----------------------- Gaussian Process Models
+\section{Gaussian Process Models}
+
+\breakingframe{
+\begin{textblock*}{13cm}[0.5,0.5](0.7\textwidth,  0.5\textheight)
+\Huge\textbf{\textcolor{black}{Gaussian Process Models}}
+\end{textblock*}
+}
+
+\subsection{Conventional Gaussian Processes}
+
+\begin{frame}
+    \begin{block}{Definition}
+        A Gaussian Process is a collection of random variables, any finite
+        number of which have a joint Gaussian distribution.
+    \end{block}
+    \begin{block}{Mathematical formulation}
+        \begin{equation*}
+                \begin{aligned}
+                    m(\mathbf{x}) &= \mathbb{E}[f(\mathbf{x})] \\
+                    k(\mathbf{x}, \mathbf{x'}) &= \mathbb{E}[f(\mathbf{x} -
+                    m(\mathbf{x}))(f(\mathbf{x'}) - m(\mathbf{x'}))]
+                \end{aligned}
+        \end{equation*}
+    \end{block}
+    \note[item]{The formal definition of a Gaussian Process states that it is a
+    collection of random variables, any finite number of which have a joint
+    Gaussian distribution.}
+    \note[item]{Another useful way of thinking of GPs is as a probability distribution, but over functions rather than variables. This is a really useful thing, as often in machine learning what we are trying to do is some form of function approximation. A GP allows us to derive posterior distributions over functions by simply observing variables.}
+\end{frame}
+
+\begin{frame}
+    \frametitle{Benefits}
+    \begin{itemize}
+        \item Provide a complete Gaussian distribution for a predicted value
+            \vspace{10pt} \pause
+        \item Capture complex system behaviour with less data \vspace{10pt}
+            \pause
+        \item Include prior beliefs and impose desired model behaviour
+            \vspace{10pt} \pause
+            \begin{itemize}
+                \item Different kernels can lead to linear, periodic, smooth
+                    functions \vspace{10pt}
+                \item Combinations of multiple kernel functions can impose
+                    arbitrary behaviour \vspace{10pt}
+                \item Ability to impose a prior distribution on hyperparameters
+                    before training \vspace{10pt}
+            \end{itemize}
+    \end{itemize}
+\end{frame}
+
+\begin{frame}
+    \frametitle{Shortcomings}
+
+    \begin{block}{Predicting new values}
+        \begin{equation*}
+                \begin{aligned}
+                    \mathbf{f_*} = \mathbb{E}\left(f_*|X, \mathbf{y}, X_*\right) &=
+                    K_*\left(K + \sigma_n^2I\right)^{-1}\mathbf{y} \\
+                    cov(\mathbf{f_*}) &= K_{**} - K_*\left(K +\sigma_n^2I\right)^{-1}K_*^T \\
+                \end{aligned}
+        \end{equation*}
+    \end{block}
+
+    \begin{block}{Maximum likelihood}
+        \begin{equation*}
+                \log(p(y)) = - \frac{1}{2}\log{\left(
+                                \det{\left(
+                                        K + \sigma_n^2I
+                                \right)}
+                            \right)}
+                - \frac{1}{2}y^T\left(
+                                    K + \sigma_n^2I
+                                \right)^{-1}y
+                - \frac{n}{2}\log{\left(2\pi\right)}
+        \end{equation*}
+    \end{block}
+
+    \pause
+    \begin{itemize}
+        \item $\mathcal{O}(n^3)$ time for evaluation
+        \item $\mathcal{O}(n^4)$ time for training
+        \item $\mathcal{O}(n^2)$ space for finished model
+    \end{itemize}
+    \note[item]{Both training and evaluation require inversion of the covariance
+    matrix}
+    \note[item]{Impractical for embedded computers (slow, little memory)}
+    \note[item]{Impractical for systems with faster dynamics}
+    \note[item]{Impractical for complex systems where more data is needed to
+    capture model behaviour}
+\end{frame}
+
+\subsection{Sparse and Variationsl Gaussian Processes}
+
+\begin{frame}
+    \frametitle{Sparse and Variational Gaussian Processes}
+    Extension of classical Gaussian Processes for use on larger scale datasets
+    \pause
+    \begin{block}{Sparse}
+        Approximating the full training dataset with a smaller number of points:
+        \\
+        \quad \textit{Inducing random variables} $f(X_s)$ at \textit{inducing
+        locations} $X_s$
+    \end{block}
+    \pause
+    \begin{block}{Variational}
+    Variational inference uses the \textit{variational
+    distribution} $q(f, f_s)$ to approximate the true posterior $p(f, f_s|y)$ \\
+    This approximation leads to the \textit{Evidence Lower Bound} (ELBO), used
+    for parameter training
+    \end{block}
+    \note[item]{Extension of classical GP meant to aleviate its shortcomings}
+    \note[item]{Inducing random variables are a new set of learnable parameters
+    trained in such a way to generate the original dataset as close as possible.
+They are trained at the same time as the model, and when the original inputs are
+evaluated on this new model the outputs should as close as possible ressemble
+the original dataset outputs}
+    \note[item]{With variational inference we approximate the true posterior
+    distribution of the Gaussian process with the variational distribution}
+    \note[item]{ELBO approximation allows training of the model on subsets
+    (minibatches) of the original data}
+\end{frame}
+
+
+% ----------------------- CARNOT Model
+\section{CARNOT Model}
+
+\breakingframe{
+\begin{textblock*}{13cm}[0.5,0.5](0.7\textwidth,  0.5\textheight)
+\Huge\textbf{\textcolor{black}{CARNOT Building Model}}
+\end{textblock*}
+}
+
+\begin{frame}
+    \frametitle{Motivation}
+    \begin{block}{Using CARNOT model as plant}
+        \vspace{10pt}
+        \begin{itemize}
+            \item Much faster than real-time simulations \vspace{10pt}
+                % allow for easier long-term performance evaluations
+            \item Reproducible weather/ disturbances \vspace{10pt}
+                % allows a much more direct comparison of different model
+                % performances
+        \end{itemize}
+    \end{block}
+
+    \begin{block}{Using the real Polydome building as basis}
+        Experimental data already available
+        \vspace{10pt}
+        \begin{itemize}
+            \item  Good baseline for comparing the CARNOT model to a real
+                building \vspace{10pt}
+            \item  Path to easier implementation of same control scheme on the
+                real Polydome \vspace{10pt}
+        \end{itemize}
+    \end{block}
+\end{frame}
+
+\subsection{The Polydome building}
+
+\begin{frame}
+    \frametitle{Geometrical parameters}
+    % TODO: [CARNOT] Geometrical parameters of the Polydome
+    \begin{columns}
+        \begin{column}{0.3\textwidth}
+            \centering
+            \includegraphics[height=\textwidth]{Images/google_maps_polydome_skylights.png}
+        \end{column}
+        \begin{column}{0.7\textwidth}
+            \centering
+            \includegraphics[height=0.45\textwidth]{Images/polydome_streetview_annotated.png}
+        \end{column}
+    \end{columns}
+
+    \note[item]{Base geometrical dimensions from an architectural journal
+    article on the Polydome construction:
+        \begin{itemize}
+            \item Spherical dome shape with a mostly square base of size 25m $\times$
+                25m
+            \item Total building height of around 7 meters
+        \end{itemize}
+    }
+    \note[item]{Confirmation of surface from google maps, as well as
+    approximation of skylights shape\vspace{10pt}}
+    \note[item]{Overall building approximated with a spherical dome on top of a
+    cylindrical stem wall}
+    \note[item]{Google Street View capture of the Polydome building. An object
+    of known dimensions is used (HVAC) as a scale and the necessary dimensions
+    are measured with the Measure Tool in GIMP
+        \begin{itemize}
+            \item Steam wall size
+            \item Dome height
+            \item Total building height (used for validation of results)
+        \end{itemize}
+    }
+\end{frame}
+
+\begin{frame}
+    \begin{block}{Materials used in the Polydome}
+    \vspace{10pt}
+    \begin{itemize}
+        \item Walls are replaced with large, top to bottom windows \vspace{10pt}
+        \item Roof made of insulation, enclosed by wood on each side
+            \vspace{10pt}
+        \item Floor consists of wood, insulation, concrete \vspace{10pt}
+    \end{itemize}
+    \end{block}
+    \pause
+    \begin{block}{Furniture}
+        Approximated to a wall made out of \textit{equivalent indoor content
+        material} with material properties and geometrical dimension to emulate
+        real furniture.
+    \end{block}
+
+    \note[item]{Materials used in Polydome}
+    \note[item]{Furniture is an important factor in building thermal inertia. In
+    this case the existing furniture has been approximated to a wall with
+geometrical and material properties to best emulate the real furniture}
+    \note[item]{Furniture material parameters come from a study on the influence
+    of furniture content on building thermal inertia and are representative of
+an office environment}
+\end{frame}
+
+\subsection{CARNOT Model overview}
+
+\begin{frame}
+    \includegraphics[height=\textheight]{Images/polydome_room_model.pdf}
+    \note[item]{Four of the five window nodes represent the building walls}
+    \note[item]{An additional window accounts for the skyboxes on the building
+    roof\vspace{10pt}}
+    \note[item]{Roof and floor made out of the appropriate materials}
+    \note[item]{A wall with the purpose of approximating the furniture content
+    of the building\vspace{10pt}}
+    \note[item]{The heat radiator assumed to be ideal}
+\end{frame}
+
+
+% ----------------------- MPC Problem
+\section{The MPC Problem}
+
+\breakingframe{
+\begin{textblock*}{13cm}[0.5,0.5](0.75\textwidth,  0.5\textheight)
+\Huge\textbf{\textcolor{black}{The MPC Problem}}
+\end{textblock*}
+}
+
+\begin{frame}
+    \begin{block}{The Optimisation Problem}
+    \begin{equation*}
+            \begin{aligned}
+                & \text{minimize}
+                & & \sum_{i=0}^{N-1} (\bar{y}_{t+i} - y_{ref, t})^2 \\
+                & \text{subject to}
+                & & \bar{y}_{t+i} = K_*K^{-1}\mathbf{x}_{t+i-1} \\
+                &&& \mathbf{x}_{t+i-1} = \left[\mathbf{w}_{t+i-1},\quad
+                \mathbf{u}_{t+i-1},\quad \mathbf{y}_{t+i-1}\right]^T \\
+                \label{eq:components}
+                &&& u_{t+i} \in \mathcal{U}
+            \end{aligned}
+    \end{equation*}
+    \end{block}
+    \note[item]{The Problem of tracking a reference temperature subject to:
+        \begin{itemize}
+            \item Model constraints
+            \item Future disturbance inputs
+            \item Allowed input range (HVAC heating/cooling capacity)
+        \end{itemize}
+    }
+    \note[item]{Choosing this specific optimisation problem allows easier
+    comparison of different model performances, since they are directly
+following the reference temperature}
+\end{frame}
+
+\begin{frame}
+    \frametitle{Reference temperature}
+    \centering
+    \includegraphics[height=0.75\textheight]{Images/sia_180_2014.png}
+    \note[item]{Tracking the mean of the SIA 180:2014 reference temperature
+    range for residental buildings. It is computed using a rolling window of
+    the last 48 hours of outside temperature measurement\vspace{10pt}}
+    \note[item]{Choosing this as a reference temperature provides a more
+    realistic simulation scenario, as well as allowes to analyse model
+    performance for a larger range of operating temperatures}
+\end{frame}
+
+% ----------------------- Implementation
+\section{Implementation}
+
+\breakingframe{
+\begin{textblock*}{5cm}[0.5,0.5](0.5\textwidth,  0.5\textheight)
+\Huge\textbf{\textcolor{black}{Implementation}}
+\end{textblock*}
+}
+
+\begin{frame}
+    \frametitle{Complete diagram}
+    \centering
+    \includegraphics[height=0.75\textheight]{Images/setup_diagram.pdf}
+    \note[item]{The two basic building blocks of the simulation are:
+        \begin{itemize}
+            \item The building model and weather prediction built in CARNOT/Simulink
+            \item The control scheme implemented in Python
+        \end{itemize}
+    }
+    \note[item]{The server starts by implementing a PI controller
+    tracking the defined reference temperature until enough data has been
+collected. At that point the GP model is trained and the server switches to the
+MPC controller going forward}
+    \note[item]{The python server is also responsible of keeping track of when
+    to re-train the model in the case of adaptive schemes}
+\end{frame}
+
+\begin{frame}
+    \frametitle{Simulink Diagram}
+    \centering
+    \includegraphics[height=0.75\textheight]{Images/polydome_python.pdf}
+    \note[item]{The Simulink model and Python server interface through three
+    independent TCP/IP sockets, each responsible for tranmission of the control
+signal, measurement of the output values and the weather prediction}
+\end{frame}
+
+\begin{frame}
+    \frametitle{GP implementation in Python}
+    \begin{block}{GP implementation}
+        \vspace{10pt}
+        \begin{itemize}
+            \item GP and SVGPs implemented with GPflow and Tensorflow \vspace{10pt}
+            \item Optimization Problem implemented with CasADi \vspace{10pt}
+        \end{itemize}
+    \end{block}
+
+    \begin{block}{Average computation time}
+        \vspace{10pt}
+        \begin{itemize}
+            \item Classical GP optimisation step of around 1-2 s \vspace{10pt}
+            \item SVGP optimisation step of around 200-300 ms \vspace{10pt}
+        \end{itemize}
+    \end{block}
+
+    \note[item]{Both libraries provide very efficient implementation of all the
+    required functions, leading to short computation times}
+\end{frame}
+
+% ----------------------- Simulations
+\section{Full-year simulations}
+
+\breakingframe{
+\begin{textblock*}{13cm}[0.5,0.5](0.75\textwidth,  0.5\textheight)
+\Huge\textbf{\textcolor{black}{Full-year simulations}}
+\end{textblock*}
+}
+
+\begin{frame}
+    \frametitle{GP implementations}
+    \begin{block}{GP implementations for full-year simulations}
+        \vspace{10pt}
+        \begin{itemize}
+            \item Classical GP model trained on the five days of identification
+                data \vspace{10pt}
+            \item SVGP model trained on five days of identification data
+                \vspace{10pt}
+            \item SVGP model trained on one day of identification data
+                \vspace{10pt}
+            \item SVGP model trained on a rolling window of five days of
+                closed-loop operation data \vspace{10pt}
+        \end{itemize}
+    \end{block}
+\end{frame}
+
+\begin{frame}
+    \frametitle{Classical GP full year simulation}
+    \centering
+    \includegraphics[width=0.85\textwidth]{Plots/4_GP_480pts_12_averageYear_fullyear.pdf}
+    \note[item]{From the first result it can be seen that the classical GP does
+    not perform well. It has a very large offset from the start of the
+simulation and becomes completely unstable in late summer}
+\end{frame}
+
+\begin{frame}
+    \frametitle{Absolute Error graph}
+    \centering
+    \includegraphics[width=\textwidth]{Plots/4_GP_480pts_12_averageYear_abserr.pdf}
+    \note[item]{A more quantitative analysis shows a maximum absolute error of
+    aroun 25 degrees C, with the mean over the whole year being 1.33 degrees C}
+\end{frame}
+
+\begin{frame}
+    \frametitle{GP model performance}
+    \centering
+    \includegraphics[width=\textwidth]{Plots/4_GP_480pts_12_averageYear_first_model_performance.pdf}
+    \note[item]{Very good multistep ahead performance in the training region,
+    the model correctly reproduces learned data}
+    \note[item]{At step 500 the model is able to correctly predict the heating
+    of the building to the 22.5 degrees C reference temperature}
+    \note[item]{Already at step 750, on the ninth day of the simulation, the
+    model is unable to properly predict building behaviour and settles on a
+    steady-state prediction error of ~0.75 degrees C.}
+    \note[item]{Even worse performance at experimental step 1000, where the
+    steady-state error is around 1.5 degrees C}
+\end{frame}
+
+\begin{frame}
+    \frametitle{Disturbance signal}
+    \centering
+    \includegraphics[width=\textwidth]{Plots/Exogenous_inputs_fullyear.pdf}
+    \note[item]{The weather patterns are representative of Switzerland, with
+    generally mild winters and temperate summer, but the weather does not remain
+constant throughout the year\vspace{10pt}}
+    \note[item]{Both disturbance inputs, the outside temperature and the global
+    irradiation are outside the learning dataset region already around the 500
+point mark}
+    \note[item]{This forces the GP model to work in an extrapolated region of
+    the state space, which it did not see during training. In this situation the
+GP model does not perform well\vspace{10pt}}
+    \note[item]{The window of values for the two disturbance signals keeps
+    expanding until mid summer, after which both values start decreasing again.
+This is useful for training the SVGP models.}
+\end{frame}
+
+
+\begin{frame}
+    \frametitle{SVGP full year simulation}
+    \centering
+    \includegraphics[width=0.85\textwidth]{Plots/1_SVGP_480pts_inf_window_12_averageYear_fullyear.pdf}
+    \note[item]{Much better performance than the classical GP system}
+    \note[item]{The only large deviations from the reference temperatures are in
+    the winter, when the HVAC heat supply is at its limit.}
+    \note[item]{The constant model updates mean that the model does not have to
+    extrapolate as far in the unknown regions before new data is added}
+\end{frame}
+
+\begin{frame}
+    \frametitle{Absolute Error graph}
+    \centering
+    \includegraphics[width=\textwidth]{Plots/1_SVGP_480pts_inf_window_12_averageYear_abserr.pdf}
+    \note[item]{Quantitavely a much better result, with a maximum absolute error of
+    around 1.6 degrees, except the cold days limited by the HVAC power}
+    \note[item]{An average absolute error over the whole year of ~0.055 degrees
+    C}
+\end{frame}
+
+\begin{frame}
+    \frametitle{SVGP model performance}
+    \centering
+    \movie[width=\textwidth]{
+        \includegraphics[width=\textwidth]{Plots/1_SVGP_480pts_inf_window_12_averageYear_model_0_performance.pdf}}
+        {Plots/SVGP_perf_animation.mkv}
+    \note[item]{Play the simulation movie}
+    \note[item]{Overall two large families of models. During the first part of
+    the year, as the range of the weather data gets expanded the predictions get
+progressively better. For the second part of the year the range of the data does
+not get expanded anymore and the performance of the model becomes noticeably
+better}
+    \note[item]{The multistep prediction performance of the SVGP over the
+    training region (ie. at 250 steps) starts much worse than that of the
+equivalent GP. This could be a sign that more inducing variables are necessary
+to properly reproduce the training data}
+\end{frame}
+
+\begin{frame}
+    \frametitle{SVGP one day starting data}
+    \centering
+    \includegraphics[width=0.85\textwidth]{Plots/6_SVGP_96pts_inf_window_12_averageYear_fullyear.pdf}
+    \note[item]{Performance very comparable to that of five days initial model}
+    \note[item]{This hints at the fact that SVGP models can be deployed using
+    much less initial training data than traditional GP models, and are still
+capable of good performance from learned behaviour}
+\end{frame}
+
+\begin{frame}
+    \frametitle{SVGP five day rolling window}
+    \centering
+    \includegraphics[width=0.85\textwidth]{Plots/5_SVGP_480pts_480pts_window_12_averageYear_fullyear.pdf}
+    \note[item]{Five days worth of initial training data. After five days of
+    operation, the rolling window of training data does not contain any initial
+    identification anymore, only closed loop operation data. This information turns
+    out to be insufficient for learning the plant behaviour and the controller
+    becomes unstable.}
+    \note[item]{The additional excitation of the model in turn provides enough
+    information for the next model to properly capture its behaviour, turning
+    the controller stable again until the data containing the excitations is too old
+    again to include in the training set.}
+\end{frame}
+
+\begin{frame}
+    \frametitle{SVGP linear kernel}
+    \centering
+    \includegraphics[width=0.85\textwidth]{Plots/10_SVGP_480pts_inf_window_12_averageYear_LinearKernel_fullyear.pdf}
+    \note[item]{This model is still stable and able to roughly follow the
+    reference temperature. It has, however poorer performance than the main
+model, trained using a Squared Exponential Kernel. This means that the Linear
+Kernel is too simplistic for even this situation.}
+\end{frame}
+
+% ----------------------- Future work
+\section{Future Work}
+
+\breakingframe{
+\begin{textblock*}{10cm}[0.5,0.5](0.75\textwidth,  0.5\textheight)
+\Huge\textbf{\textcolor{black}{Future work}}
+\end{textblock*}
+\note[item]{Several situations have not been thoroughly addressed in this
+work and could be further investigated, as well as multiple directions for
+direct continuation of this project are possible}
+}
+
+\begin{frame}
+    \frametitle{Future work}
+    \begin{itemize}
+        \item A more varied initial dataset for the classical Gaussian Process
+            \vspace{10pt} \pause
+        \item Smart update of a fixed-size data dictionary according to
+            information gain \vspace{10pt} \pause
+        \item Sparse GP wihout the use of variational inference \vspace{10pt}
+            \pause
+
+        \item The size of the inducing variables set can be further optimized
+            \vspace{10pt} \pause
+
+        \item More specialized kernel functions can be very beneficial in the
+            case of SVGP models
+    \end{itemize}
+
+    \note[item]{Varied initial dataset can be more representative of the
+    plant operating region over long timespans, improving overall model quality
+    \vspace{10pt}}
+
+    \note[item]{Keeping a dictionary will inevitably aleviate some of the
+    downsides of using classical Gaussian Processes, at the cost of much more
+    expensive computations for model update
+    \vspace{10pt}}
+
+    \note[item]{Not using variational inference in the form of the Evidence
+    Lower Bound can provide a model that better explains the training data, at
+    the expense of longer training time}
+
+    \note[item]{More complex are refined kernel functions can greatly improve
+    behaviour in the case of SVGP models as they are less capable of capturing
+    plant dynamics as the classical GP counterpart, given the same training dataset}
+
+\end{frame}
+
+
+% -----------------------References
+% Thank you slide should be here
+\breakingframe{
+\begin{textblock*}{10cm}(3.2cm,4cm)
+\Huge\textbf{\textcolor{black}{Thank you for your attention}}
+\end{textblock*}
+}
+\breakingframe{
+\begin{textblock*}{10cm}(3.2cm,4cm)
+\Huge\textbf{\textcolor{black}{Questions}}
+\end{textblock*}
+}
+% -----------------------References
+\section{Bibliography}
+% \begin{frame}[allowframebreaks]{\\References}\vspace{4pt}
+\begin{frame}{References}\vspace{4pt}
+\tiny{\printbibliography}
+\end{frame}
+\normalsize

Sections/slides_metadata.tex

@@ -0,0 +1,21 @@
+% ---- Add your Meta-data to the PDF (Copyrights Kinda!) ----
+\hypersetup{
+  pdfinfo={
+    Title={Inter-seasonal Performance of Gaussian
+Process-based Model Predictive Control of
+Buildings},
+    Author={Radu C. Martin},
+    Subject={EPFL - IGM - LA3 Lab},
+    Keywords={Model Predictive Control, Gaussian Process, Sparse Variational
+    Gaussian Process}
+  }
+}
+
+\author{Radu C. Martin}
+\title[Inter-seasonal Performance of GP-based MPC of Buildings]
+    {Inter-seasonal Performance of Gaussian Process-based Model Predictive Control of Buildings}
+
+\institute[IGM]{{\'Ecole Polytechnique F\'ed\'erale de Lausanne
+(EPFL)}{\newline\newline Institute of Mechanical Engineering (IGM)}}
+\subject{Master Thesis Defense}
+\date{\today}

slides_clean.tex

@@ -0,0 +1,50 @@
+\documentclass{EESD}
+% To change the slides size go to EESD.cls file and edit the preamble as explained.
+
+% Important packages to be called
+\usepackage{subcaption} % for adding sub-figures
+\usepackage{graphicx}
+\usepackage{tikz} % for cool graphics and drawings
+\usepackage{multimedia} % for embedded multimedia files
+\usepackage[final]{pdfpages} % include pdf figures
+
+\usepackage[absolute,overlay]{textpos} % To place the figures by coordinates (x,y) - Beamer doesn't support floats XD
+\usepackage{multicol} % To adjust items and stuff automatically in a number of a pre-specified columns
+\graphicspath{{Figures/}}
+\usepackage[utf8]{inputenc}
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{amssymb}
+\usepackage{lipsum} % Just a dummy text generator
+\usepackage{hyperref}
+% fonts packages
+\usepackage{ragged2e} % Justified typesetting
+
+% For References Only
+\usepackage[style=authortitle,backend=bibtex]{biblatex}
+\addbibresource{references.bib} % Call the references database
+\AtBeginBibliography{\tiny} % Specify font size (Size matters)
+\renewcommand{\footnotesize}{\tiny}
+
+% For adding code blocks
+\usepackage{listings}
+\lstset
+{
+    language=[LaTeX]TeX,
+    breaklines=true,
+    basicstyle=\tt\scriptsize,
+    keywordstyle=\color{blue},
+    identifierstyle=\color{magenta},
+    commentstyle=\color{red},
+    rulecolor=\color{black},
+    numbers=left,
+    numberstyle=\tiny\color{black},
+    % framexleftmargin=15pt,
+    frame = single,
+}
+
+\include{Sections/slides_metadata.tex}
+
+\begin{document}
+    \include{Sections/slides_content.tex}
+\end{document}

slides_notes.tex

@@ -0,0 +1,53 @@
+\documentclass{EESD}
+% To change the slides size go to EESD.cls file and edit the preamble as explained.
+
+% Show notes on second screen
+\setbeameroption{show notes on second screen=right}
+
+% Important packages to be called
+\usepackage{subcaption} % for adding sub-figures
+\usepackage{graphicx}
+\usepackage{tikz} % for cool graphics and drawings
+\usepackage{multimedia} % for embedded multimedia files
+\usepackage[final]{pdfpages} % include pdf figures
+
+\usepackage[absolute,overlay]{textpos} % To place the figures by coordinates (x,y) - Beamer doesn't support floats XD
+\usepackage{multicol} % To adjust items and stuff automatically in a number of a pre-specified columns
+\graphicspath{{Figures/}}
+\usepackage[utf8]{inputenc}
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{amssymb}
+\usepackage{lipsum} % Just a dummy text generator
+\usepackage{hyperref}
+% fonts packages
+\usepackage{ragged2e} % Justified typesetting
+
+% For References Only
+\usepackage[style=authortitle,backend=bibtex]{biblatex}
+\addbibresource{references.bib} % Call the references database
+\AtBeginBibliography{\tiny} % Specify font size (Size matters)
+\renewcommand{\footnotesize}{\tiny}
+
+% For adding code blocks
+\usepackage{listings}
+\lstset
+{
+    language=[LaTeX]TeX,
+    breaklines=true,
+    basicstyle=\tt\scriptsize,
+    keywordstyle=\color{blue},
+    identifierstyle=\color{magenta},
+    commentstyle=\color{red},
+    rulecolor=\color{black},
+    numbers=left,
+    numberstyle=\tiny\color{black},
+    % framexleftmargin=15pt,
+    frame = single,
+}
+
+\include{Sections/slides_metadata.tex}
+
+\begin{document}
+    \include{Sections/slides_content.tex}
+\end{document}

thesis.tex

@@ -100,10 +100,11 @@ Model Predictive Control of Buildings}
 \usepackage{fancyhdr}
 \pagestyle{fancy}
 \setlength\headheight{35pt}
-\setlength\footskip{13.6pt}
+\setlength\footskip{27pt}
 \fancyhf{Inter-seasonal GP MPC control for buildings}
 \rhead{\includegraphics[width=2cm]{Logo-EPFL.png}}
 \lhead{}
+%\renewcommand{\footrulewidth}{0.1pt}
 \cfoot{\thepage}
 
 \usepackage[framed,numbered,autolinebreaks,useliterate]{mcode}
@@ -121,7 +122,7 @@ Model Predictive Control of Buildings}
 \begin{document}
 \selectlanguage{english}
 
-\input{00_First_Page.tex}
+\input{Sections/00_First_Page.tex}
 
 \tableofcontents
 \clearpage
@@ -129,16 +130,16 @@ Model Predictive Control of Buildings}
 \printnoidxglossary[type=\acronymtype]
 \clearpage
 
-\input{10_Introduction.tex}
+\input{Sections/10_Introduction.tex}
-\input{30_Gaussian_Processes_Background.tex}
+\input{Sections/30_Gaussian_Processes_Background.tex}
-\input{40_CARNOT_model.tex}
+\input{Sections/40_CARNOT_model.tex}
-\input{50_Choice_of_Hyperparameters.tex}
+\input{Sections/50_Choice_of_Hyperparameters.tex}
-\input{60_The_MPC_Problem.tex}
+\input{Sections/60_The_MPC_Problem.tex}
-\input{70_Implementation.tex}
+\input{Sections/70_Implementation.tex}
-\input{80_Results.tex}
+\input{Sections/80_Results.tex}
-\input{90_Conclusion.tex}
+\input{Sections/90_Conclusion.tex}
 \printbibliography[heading=bibintoc]
 \appendix
-\input{99A_GP_hyperparameters_validation.tex}
+\input{Sections/99A_GP_hyperparameters_validation.tex}
-\input{99C_hyperparameters_results.tex}
+\input{Sections/99C_hyperparameters_results.tex}
 \end{document}