include first image for 4.1.1

chapters/chap04/chap04.tex

@@ -9,17 +9,37 @@
 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \chapter{Experiments   10}
 \label{chap:evaluation}
+In the previous chapters we explained the methods (see~\Cref{chap:methods})
+based the theoretical background, that we established in~\Cref{chap:background}.
+In this chapter, we present the setups and results from the experiments and
+simulations, we ran. First, we tackle the experiments dedicated to find the
+epidemiological parameters of $\beta$ and $\alpha$ in synthetic and real-world
+data. Second, we identify the reproduction number in synthetic and real-world
+data of Germany. Each section, is divided in the setup and the results of the
+experiments.
 
 % -------------------------------------------------------------------
 
-\section{SIR Model   5}
+\section{Identifying the Transition Rates on Real-World and Synthetic Data  5}
 \label{sec:sir}
+In this section we seek to find the transmission rate $\beta$ and the recovery
+rate $\alpha$ from either synthetic or preprocessed real-world data. The
+methodology that we employ to identify the transition rates is described
+in~\Cref{sec:pinn:sir}.
 
 % -------------------------------------------------------------------
 
 \subsection{Setup   1}
 \label{sec:sir:setup}
 
+\begin{figure}[h]
+    \centering
+    \includegraphics[width=0.3\textwidth]{SIR_synth.pdf}
+    \caption{Visualization of the synthetic data for the SIR model, parameters for creation:
+        $\alpha=\nicefrac{1}{3}$, $\beta=\nicefrac{1}{2}$}
+    \label{fig:synthetic_SIR}
+\end{figure}
+
 % -------------------------------------------------------------------
 
 \subsection{Results    4}