start of 2. results

chapters/chap04/chap04.tex

@@ -201,6 +201,9 @@ has the lowest $\sigma$.\\
 \begin{figure}[t]
     \centering
     \includegraphics[width=\textwidth]{mean_std_alpha_beta_res.pdf}
+    \caption{Visualization of the mean $\mu$ and standard deviation $\sigma$ of
+        the transition rates $\alpha$ and $\beta$ for each state compared to the
+        mean values of $\alpha$ and $\beta$ for Germany.}
     \label{fig:alpha_beta_mean_std}
 \end{figure}
 
@@ -280,24 +283,21 @@ we restrict the data points to an interval of 1200 days, beginning on March 09.
     \begin{subfigure}{0.3\textwidth}
         \centering
         \includegraphics[width=\textwidth]{I_synth.pdf}
-        \caption{Synthetic data}
-        \label{fig:synthetic_I}
     \end{subfigure}
     \quad
     \begin{subfigure}{0.3\textwidth}
         \centering
         \includegraphics[width=\textwidth]{I_synth_r_t.pdf}
-        \caption{Synthetic data}
-        \label{fig:synthetic_I_r_t}
     \end{subfigure}
     \vskip\baselineskip
     \begin{subfigure}{0.67\textwidth}
         \centering
         \includegraphics[width=\textwidth]{datasets_states/Germany_datasets.pdf}
-        \caption{}
-        \label{fig:germany_I_14}
     \end{subfigure}
-
+    \caption{The upper two graphics show the curve of the size of the
+        infectious group (left) and the corresponding true reproduction value
+        $\Rt$ (right) for the synthetic data. The lower graphic exemplary
+        illustrates the different curves for Germany.}
 \end{figure}
 
 In order to achieve the desired output, the selected neural network
@@ -319,7 +319,11 @@ reduced SIR model and the reproduction number $\Rt$. First, we present
 our findings for the synthetic dataset. Then, we provide and discuss the
 results for the real-world data.\\
 
-In~\Cref{fig:synth_results}
+\Cref{fig:synth_results} illustrates that the model successfully learns the
+synthetic training data, with an error of $e_{\text{synth}} = 0.0016$. Meanwhile,
+the prediction for the reproduction number $\Rt$ for the synthetic data, is accuracy,
+while having by far the highest standard deviation in the first 30 days. The
+error concerning the reproduction number is $e_{\Rt} = 0.0521$.
 
 \begin{figure}[t]
     \centering
@@ -331,7 +335,10 @@ In~\Cref{fig:synth_results}
         \includegraphics[width=\textwidth]{synthetic_R_t_statistics.pdf}
     \end{subfigure}
     \label{fig:synth_results}
-    \caption{text}
+    \caption{Results for the reproduction rate $\Rt$ on synthetic data. The
+        left graphic show the prediction of the model regarding the $I$ group. The
+        right graphic presents the predicted $\Rt$ against the true value, with the
+        standard deviation.}
 \end{figure}
 
 \begin{figure}[t]
@@ -343,7 +350,6 @@ In~\Cref{fig:synth_results}
     \begin{subfigure}{0.45\textwidth}
         \includegraphics[width=\textwidth]{Germany_I_prediction.pdf}
     \end{subfigure}
-
     \vskip\baselineskip
     \begin{subfigure}{0.45\textwidth}
         \includegraphics[width=\textwidth]{R_t/Sachsen_Anhalt_R_t_statistics.pdf}