Added Presentation tex files
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EESD.cls
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EESD.cls
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% Mahmoud S. Shaqfa - EESD lab. - EPFL
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% Email: mahmoud.shaqfa@epfl.ch
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\NeedsTeXFormat{LaTeX2e}
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\ProvidesClass{EESD}
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\LoadClass[aspectratio = 169, 11pt, xcolor={usenames,dvipsnames}]{beamer}
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% 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
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% Other possible values are: 1610, 149, 54, 43 and 32.
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% \documentclass[aspectratio=1610]{beamer}
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% Sets aspect ratio to 16:10, and frame size to 160mm by 100mm.
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% 77
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% \documentclass[aspectratio=169]{beamer}
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% Sets aspect ratio to 16:9, and frame size to 160mm by 90mm.
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% \documentclass[aspectratio=149]{beamer}
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% Sets aspect ratio to 14:9, and frame size to 140mm by 90mm.
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% \documentclass[aspectratio=141]{beamer}
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% Sets aspect ratio to 1.41:1, and frame size to 148.5mm by 105mm.
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% \documentclass[aspectratio=54]{beamer}
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% Sets aspect ratio to 5:4, and frame size to 125mm by 100mm.
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% \documentclass[aspectratio=43]{beamer}
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% The default aspect ratio and frame size to 128mm by 96mm. You need not specify this option.
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% \documentclass[aspectratio=32]{beamer}
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% Sets aspect ratio to 3:2, and frame size to 135mm by 90mm.
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% ---- My Colors Specifiers ----
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\definecolor{mypink}{rgb}{0.97, 0.56, 0.65}
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\definecolor{myviolet}{rgb}{0.6, 0.4, 0.8}
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\definecolor{myblue}{rgb}{0.61, 0.77, 0.89}
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\definecolor{green1}{rgb}{0.00, 0.45, 0.47} % darker green
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\definecolor{green2}{rgb}{0.73, 0.88, 0.82} % light green
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\definecolor{violet1}{rgb}{0.59, 0.08, 0.39} % darker violet
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\definecolor{violet2}{rgb}{0.85, 0.78, 0.85} % light violet
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\setbeamercolor*{header color}{fg=white,bg=black}
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\setbeamercolor*{footer color1}{fg=black}%,bg=beamerfooter1} % pink
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\setbeamercolor*{footer color2}{fg=white}%,bg=beamerfooter2} % dark pink
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\setbeamercolor*{footer color3}{fg=white}%,bg=beamerfooter3} % dark red
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\setbeamertemplate{blocks}[rounded][shadow=true]
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\setbeamercolor{block body}{fg = black, bg = beamerfooter1}
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\setbeamercolor{block title}{fg=white, bg=beamerfooter2}
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\setbeamercolor{block body example}{fg = black, bg = green2}
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\setbeamercolor{block title example}{fg = white, bg = green1}
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\setbeamercolor{block body alerted}{fg = black, bg = violet2}
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\setbeamercolor{block title alerted}{fg=white, bg=violet1}
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\pgfdeclarehorizontalshading[beamerfooter1,beamerfooter2,beamerfooter3]
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{beamer@frametitleshade}{\paperheight}{
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color(0pt)=(beamerfooter3);
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color(0.3333\paperwidth)=(beamerfooter2);
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color(1.056\paperwidth)=(beamerfooter1)
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}
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\setbeamertemplate{frametitle}{\vspace{20pt}\color{beamerfooter3}\textbf\insertframetitle}
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% ---- Bibliography Specifiers ----
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\setbeamertemplate{bibliography item}[text] % Regular numbering (Formal)
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% ---- Itemize Specifier ----
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\setbeamertemplate{itemize items}[square]
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\setbeamertemplate{enumerate items}[square]
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% ---- Frame Title Specifier ----
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\addtobeamertemplate{frametitle}{}{\vspace{0pt}} % increase vspace between the title and text
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\newcommand{\rom}[1]{\uppercase\expandafter{\romannumeral #1\relax}} % Add Romans numbering
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\usecolortheme[named=beamerfooter3]{structure}
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\setbeamertemplate{headline}{}
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\setlength{\footnotesep}{0.05cm}
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% Table of contents size subsections and subsubsections
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\setbeamerfont{subsection in toc}{size=\scriptsize}
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\setbeamerfont{subsubsection in toc}{size=\scriptsize}
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% Table of contents (Enumeration shapes)
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\setbeamertemplate{section in toc}[square]
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\setbeamertemplate{subsection in toc}[square]
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\setbeamertemplate{subsubsection in toc}[square]
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\setbeamercovered{transparent} % Transparent Text When Use "Pauses"!
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\setbeamertemplate{navigation symbols}%{default}
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\logo{\centering\includegraphics[height=1.43cm]{logos169.pdf}\vspace{220pt}}
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\addtobeamertemplate{footnote}{}{\vspace{1.5ex}}
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% -------- Special frames ---------
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\newcommand{\coverpage}[1]{
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{
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\setbeamertemplate{headline}{
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\leavevmode
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\hbox{
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\begin{beamercolorbox}[wd=1.009\textwidth, ht=2.5ex, dp=1.125ex]{}
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\end{beamercolorbox}
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}
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}
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\setbeamertemplate{footline}
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{
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\leavevmode%
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\setbox\beamer@tempbox=\hbox{%
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\begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex, center]{footer color3}%
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\usebeamerfont{author in head/foot}\hspace{2ex}\insertshortauthor
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\end{beamercolorbox}%
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\begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,center]{footer color2}%
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% \usebeamerfont{title in head/foot}\insertshorttitle
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\end{beamercolorbox}%
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\begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,right]{footer color1}%
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\usebeamerfont{title in head/foot}\insertshorttitle{}\hspace*{6em}~~~~~~~~\hspace*{2ex}
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\end{beamercolorbox}%
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}%
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\beamer@tempdim=\ht\beamer@tempbox%
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\advance\beamer@tempdim by 4pt%
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\begin{pgfpicture}{0pt}{0pt}{\paperwidth}{20pt}
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\pgfpathrectangle{\pgfpointorigin}{\pgfpoint{\paperwidth}{\beamer@tempdim}}
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\pgfusepath{clip}
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\pgftext[left,base]{\pgfuseshading{beamer@frametitleshade}}
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\end{pgfpicture}
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\vskip-\beamer@tempdim%
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\box\beamer@tempbox%
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}%
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\setbeamercolor{background canvas}{}
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\begin{frame}[t, noframenumbering, allowframebreaks]{}
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#1
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\end{frame}
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}
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}
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% Define and customize the headline style of slides
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\setbeamertemplate{headline}{%
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\leavevmode%
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\hbox{%
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\begin{beamercolorbox}[wd=1.000\textwidth, ht=2.5ex, dp=1.125ex]{header color}%
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\ifx\insertsubsection\empty % no subsection
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{{~~}\insertsection}%
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\else % subsection exists
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\ifx\insertsubsubsection\empty % subsection but no subsubsection
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{~\insertsection \textcolor{white}{$~~\bullet$} ~\S~\insertsubsection}%
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\else % subsection and subsubsection exist
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{~\insertsection \textcolor{white}{$~~\bullet$} ~\S~\insertsubsection \textcolor{white}{$~~\bullet$} ~\S~\insertsubsubsection}%
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\fi
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\fi
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\end{beamercolorbox}%
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}
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}
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\newcommand{\breakingframe}[1]{
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{
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\setbeamertemplate{footline}
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{
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\leavevmode%
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\setbox\beamer@tempbox=\hbox{%
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\begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex, center]{footer color3}%
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\usebeamerfont{author in head/foot}\hspace{2ex}\insertshortauthor
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\end{beamercolorbox}%
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\begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,center]{footer color2}%
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\usebeamerfont{title in head/foot}\insertshorttitle
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\end{beamercolorbox}%
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\begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,right]{footer color1}%
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\usebeamerfont{date in head/foot}\insertshortdate{}\hspace*{6em}~~~~~~~~\hspace*{2ex}
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\end{beamercolorbox}%
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}%
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\beamer@tempdim=\ht\beamer@tempbox%
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\advance\beamer@tempdim by 4pt%
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\begin{pgfpicture}{0pt}{0pt}{\paperwidth}{20pt}
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\pgfpathrectangle{\pgfpointorigin}{\pgfpoint{\paperwidth}{\beamer@tempdim}}
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\pgfusepath{clip}
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\pgftext[left,base]{\pgfuseshading{beamer@frametitleshade}}
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\end{pgfpicture}
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\vskip-\beamer@tempdim%
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\box\beamer@tempbox%
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}%
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\setbeamercolor{background canvas}{bg=beamerfooter1}
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\begin{frame}[t, noframenumbering, allowframebreaks]{}
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#1
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\end{frame}
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}
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}
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\setbeamertemplate{footline}
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{
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\leavevmode%
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\setbox\beamer@tempbox=\hbox{%
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\begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex]{footer color3}%
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\usebeamerfont{author in head/foot}\hspace{2ex}\insertshortauthor
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\end{beamercolorbox}%
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\begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,center]{footer color2}%
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\usebeamerfont{title in head/foot}\insertshorttitle
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\end{beamercolorbox}%
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\begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,right]{footer color1}%
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\usebeamerfont{date in head/foot}\insertshortdate{}\hspace*{2em}
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\insertframenumber{} / \inserttotalframenumber\hspace*{2ex}
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\end{beamercolorbox}%
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}%
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\beamer@tempdim=\ht\beamer@tempbox%
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\advance\beamer@tempdim by 4pt%
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\begin{pgfpicture}{0pt}{0pt}{\paperwidth}{20pt}
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\pgfpathrectangle{\pgfpointorigin}{\pgfpoint{\paperwidth}{\beamer@tempdim}}
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\pgfusepath{clip}
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\pgftext[left,base]{\pgfuseshading{beamer@frametitleshade}}
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\end{pgfpicture}
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\vskip-\beamer@tempdim%
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\box\beamer@tempbox%
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}%
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BIN
Plots/1_SVGP_480pts_inf_window_12_averageYear_model_0_performance.pdf
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Plots/1_SVGP_480pts_inf_window_12_averageYear_model_0_performance.pdf
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Plots/SVGP_perf_animation.mkv
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Plots/SVGP_perf_animation.mkv
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Sections/slides_content.tex
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Sections/slides_content.tex
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{
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\coverpage{
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\titlepage{~}
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% To add additional text to the title components
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{\newline \small \textit{Supervisor}: Prof. Colin Jones \quad \textit{Assistant}: Manuel Koch \quad
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\textit{Expert}: Bratislav Svetozarevic}
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\note[item]{Introduction, welcome}
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\note[item]{Present yourself and the thesis subject}
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\note[item]{Analysis of GP models performance for longer lasting simulations, in
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this case a full year}
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\note[item]{Discussion of the shortcomngs of classical GP approaches for these
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longer experiments and possible solutions}
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}
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}
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\setbeamertemplate{logo}{} % To override the logo from the other slides and delete it completely
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% Use smart division for the TOC
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\begin{frame}{Outlines}
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\begin{multicols}{2}
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\tableofcontents
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\end{multicols}
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\note[item]{The main work consists of two parts: the CARNOT building model serving as
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a plant for the simulation, and the definition and analysis of different GP/SVGP
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based control schemes}
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\note[item]{Starting with a short introduction where the motivation for these new
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approaches is presented, followed by the basic ideas of GP models}
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\end{frame}
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% -----------------------Introduction
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\section{Introduction}
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\breakingframe{
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\begin{textblock*}{3cm}[0.5,0.5](0.5\textwidth, 0.5\textheight)
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\Huge\textbf{\textcolor{black}{Introduction}}
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\end{textblock*}
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}
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\subsection{Residential buildings}
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\begin{frame}[t]{Residential buildings energy usage}
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\begin{itemize}
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\item Residential buildings represent more than 25\% of total energy
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consumed in the EU \vspace{10pt} \pause
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\item Average of 200-300 kWh/year/m$^{2}$ \vspace{10pt} \pause
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\item Around 68\% of energy used for heating \vspace{10pt}
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\end{itemize}
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\note[item]{Residential buildings are a significant part of total energy
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consumption in the EU}
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\note[item]{Most of that energy is used for heating and ventilation of
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buildings}
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\note[item]{Additionally, there are increasing energy efficiency demands on
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new and existing buildings}
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\note[item]{Further improvements can be made by including already existing
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buildings into "smart grids"}
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\end{frame}
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\begin{frame}
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\frametitle{Limited information available}
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\begin{block}{Existing infrastructure}
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Most existing buildings already have in place Heating and Ventilation
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Systems:\pause
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\vspace{10pt}
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\begin{itemize}
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\item Limits the amount of available information \vspace{10pt} \pause
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\item Restricts the actionable signals to those provided by the existing
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HVAC \vspace{10pt}
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\end{itemize}
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\end{block}
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\pause
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\begin{block}{Weather forecast}
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Predictions of future disturbance values for the MPC also impose
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restrictions on usable data.
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\end{block}
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\note[item]{Polydome only has two temperature measurements}
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\note[item]{Existing data lacks information on air humidity}
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\note[item]{Existing data lacks information on occupancy\vspace{10pt}}
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\note[item]{The only input for the Polydome's HVAC is the setpoint
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temperature, thus only indirectly controlling the heat input\vspace{10pt}}
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\note[item]{Weather predictions are restricted to outside temperature and
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GHI}
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\note[item]{This makes the use of other disturbances, such as humidity,
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wind speed and direction, DNI, DHI inaccessible}
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\end{frame}
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\subsection{Black box models}
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\begin{frame}
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\frametitle{Black-box models}
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Data-driven models provide several practical benefits over first-principle
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models:
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\vspace{10pt}
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\begin{itemize}
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\item Foregoes complex and potentially expensive physical modelling \vspace{10pt} \pause
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\item Same data-driven model structure could be applied to other
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situations with less effort \vspace{10pt} \pause
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\item Unknown/complex plant elements, such as HVAC behaviour, unknown
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material properties , occupancy levels are much easier to include\vspace{10pt} \pause
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\end{itemize}
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\note[item]{In this context it would be very useful to be able to use
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data-driven models as they provide several benetifs over white-box
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approaches:}
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\note[item]{They forego the complex physical modelling step}
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\note[item]{Applying a control scheme using a white-box model requires a
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complete identification step, whereas for data-driven models only the
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hyperparameters have to be tuned}
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\note[item]{For buildings where not all information is readily available,
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white-box models can prove infeasible (eg. The Polydome building :D)}
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\end{frame}
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% ----------------------- Gaussian Process Models
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\section{Gaussian Process Models}
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\breakingframe{
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\begin{textblock*}{13cm}[0.5,0.5](0.7\textwidth, 0.5\textheight)
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\Huge\textbf{\textcolor{black}{Gaussian Process Models}}
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\end{textblock*}
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}
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\subsection{Conventional Gaussian Processes}
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\begin{frame}
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\begin{block}{Definition}
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A Gaussian Process is a collection of random variables, any finite
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number of which have a joint Gaussian distribution.
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\end{block}
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\begin{block}{Mathematical formulation}
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\begin{equation*}
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\begin{aligned}
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m(\mathbf{x}) &= \mathbb{E}[f(\mathbf{x})] \\
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k(\mathbf{x}, \mathbf{x'}) &= \mathbb{E}[f(\mathbf{x} -
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m(\mathbf{x}))(f(\mathbf{x'}) - m(\mathbf{x'}))]
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\end{aligned}
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\end{equation*}
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\end{block}
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\note[item]{The formal definition of a Gaussian Process states that it is a
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collection of random variables, any finite number of which have a joint
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Gaussian distribution.}
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\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.}
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\end{frame}
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\begin{frame}
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\frametitle{Benefits}
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\begin{itemize}
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\item Provide a complete Gaussian distribution for a predicted value
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\vspace{10pt} \pause
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\item Capture complex system behaviour with less data \vspace{10pt}
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\pause
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\item Include prior beliefs and impose desired model behaviour
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\vspace{10pt} \pause
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\begin{itemize}
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\item Different kernels can lead to linear, periodic, smooth
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functions \vspace{10pt}
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\item Combinations of multiple kernel functions can impose
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arbitrary behaviour \vspace{10pt}
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\item Ability to impose a prior distribution on hyperparameters
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before training \vspace{10pt}
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\end{itemize}
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\end{itemize}
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\end{frame}
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\begin{frame}
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\frametitle{Shortcomings}
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\begin{block}{Predicting new values}
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\begin{equation*}
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\begin{aligned}
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\mathbf{f_*} = \mathbb{E}\left(f_*|X, \mathbf{y}, X_*\right) &=
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K_*\left(K + \sigma_n^2I\right)^{-1}\mathbf{y} \\
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cov(\mathbf{f_*}) &= K_{**} - K_*\left(K +\sigma_n^2I\right)^{-1}K_*^T \\
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\end{aligned}
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\end{equation*}
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\end{block}
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\begin{block}{Maximum likelihood}
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\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
|
21
Sections/slides_metadata.tex
Normal file
21
Sections/slides_metadata.tex
Normal file
|
@ -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}
|
BIN
logos169.pdf
Normal file
BIN
logos169.pdf
Normal file
Binary file not shown.
50
slides_clean.tex
Normal file
50
slides_clean.tex
Normal file
|
@ -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}
|
53
slides_notes.tex
Normal file
53
slides_notes.tex
Normal file
|
@ -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}
|
Loading…
Add table
Add a link
Reference in a new issue