% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Author:   Phillip Rothenbeck
% Title:    Your Thesis
% File:     appendix/appendix.tex
% Part:     appendix
% Description:
%         summary of the content in this chapter
% Version:  19.07.2024
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\chapter{Additional Results}
\label{chap:appendix}

Here, we show the results of our experiments which we describe in~\Cref{chap:evaluation}.
Additionally, we show visualizations of the underlying dataset.

\subsection{SIR Datasets}
\label{sec:sir_datasets}
In this section, we present the datasets utilized for~\Cref{sec:sir}.~\Cref{fig:SIR_state_results_1}
and ~\Cref{fig:SIR_state_results_2} show the datasets, which we use for finding
the epidemiological parameters of $\alpha$ and $\beta$.

\begin{figure}[h!]
    \centering
    \includegraphics[width=\textwidth]{state_sir_cluster_1.pdf}
    \caption{Part 1 of the datasets, used in the experiments in~\Cref{sec:pinn:sir}.}
    \label{fig:SIR_state_results_1}
\end{figure}

\begin{figure}[h!]
    \centering
    \begin{subfigure}{\textwidth}
        \includegraphics[width=\textwidth]{state_sir_cluster_2.pdf}
    \end{subfigure}
    \quad
    \begin{subfigure}{0.35\textwidth}
        \includegraphics[width=\textwidth]{germany_single_sir.pdf}
    \end{subfigure}
    \caption{Part 2 of the datasets, used in the experiments in~\Cref{sec:pinn:sir}.}
    \label{fig:SIR_state_results_2}
\end{figure}

\subsection{$\Rt$ Results}
\label{sec:r_t_results}
Here, we present the results from our experiments in ~\Cref{sec:rsir}.
For each federal state and Germany we provide the results of the reproduction
number in the left and the corresponding dataset and the model prediction on the
right.

\begin{figure}[h!]
    \centering
    \begin{subfigure}{0.45\textwidth}
        \includegraphics[width=\textwidth]{r_t_cluster_0.pdf}
    \end{subfigure}
    \begin{subfigure}{0.45\textwidth}
        \includegraphics[width=\textwidth]{I_cluster_0.pdf}
    \end{subfigure}
    \caption{Part 1 of the results, yielded by the experiments in~\Cref{sec:pinn:rsir}.}
    \label{fig:I_state_results_1}
\end{figure}

\begin{figure}[h!]
    \centering
    \begin{subfigure}{0.45\textwidth}
        \includegraphics[width=\textwidth]{r_t_cluster_1.pdf}
    \end{subfigure}
    \begin{subfigure}{0.45\textwidth}
        \includegraphics[width=\textwidth]{I_cluster_1.pdf}
    \end{subfigure}
    \caption{Part 2 of the results, yielded by the experiments in~\Cref{sec:pinn:rsir}.}
    \label{fig:I_state_results_2}
\end{figure}

\begin{figure}[h!]
    \centering
    \begin{subfigure}{0.45\textwidth}
        \includegraphics[width=\textwidth]{r_t_cluster_2.pdf}
    \end{subfigure}
    \begin{subfigure}{0.45\textwidth}
        \includegraphics[width=\textwidth]{I_cluster_2.pdf}
    \end{subfigure}
    \caption{Part 3 of the results, yielded by the experiments in~\Cref{sec:pinn:rsir}.}
    \label{fig:I_state_results_3}
\end{figure}

\begin{figure}[h!]
    \centering
    \begin{subfigure}{0.45\textwidth}
        \includegraphics[width=\textwidth]{r_t_cluster_3.pdf}
    \end{subfigure}
    \begin{subfigure}{0.45\textwidth}
        \includegraphics[width=\textwidth]{I_cluster_3.pdf}
    \end{subfigure}
    \caption{Part 4 of the results, yielded by the experiments in~\Cref{sec:pinn:rsir}.
        The graph showing prediction of $I$ for Germany, has a different y-axis scale
        compared to all other graphs for the predictions of $I$.}
    \label{fig:I_state_results_4}
\end{figure}

