## 3 Results
### Personalization of the Model Parameters
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{\(T_{s}\)} \\ \hline \multirow{4}{*}{\
\begin{tabular}{c} Proposed \\ learning \\ method \\ \end{tabular} } & \(\frac{\text{mean}\left(\mathbf{\xi}-\mathbf{\xi}\right)\) & \(\frac{1}{4}\) & \(\left(-0.0046\right.\) & \(-0.0113\) & \(-0.0047\) & \(0.0009\) & \(-0.0009\) & \(-0.0013\) & \(-0.0019\) & \(0.0009\) & \(0.0008\right)^{\text{T}}\) \\ \cline{2-13}  & \(\text{diag}(\hat{P})\) & & \(\left(0.0371\right.\) & \(0.1350\) & \(0.0370\) & \(0.0080\) & \(0.1330\) & \(0.0399\) & \(0.1222\) & \(0.0426\) & \(0.0633\right)^{\text{T}}\) \\ \cline{2-13}  & \(\text{mean}\left(\mathbf{\xi}-\mathbf{\xi}\right)\) & \(1\) & \(\left(0.0123\right.\) & \(0.0003\) & \(0.0022\) & \(-0.0028\) & \(-0.0031\) & \(-0.0079\) & \(-0.0010\) & \(-0.0017\) & \(0.0068\right)^{\text{T}}\) \\ \cline{2-13}  & \(\text{diag}(\hat{P})\) & & \(\left(0.1009\right.\) & \(0.1679\) & \(0.0624\) & \(0.0182\) & \(0.1661\) & \(0.0618\) & \(0.2205\) & \(0.0535\) & \(0.1017\)^{\text{T}}\) \\ \hline \multirow{4}{*}{
\begin{tabular}{c} Nonlinear \\ least squares \\ method \\ \end{tabular} } & \(\frac{\text{mean}\left(\mathbf{\xi}-\mathbf{\xi}\right)\) & \(\frac{1}{4}\) & \(\left(0.1624\right.\) & \(-0.1257\) & \(-0.0205\) & \(-0.0689\) & \(0.0838\) & \(-0.0260\) & \(0.0033\) & \(0.0460\) & \(-0.0399\right)^{\text{T}}\) \\ \cline{2-13}  & \(\text{diag}(\hat{P})\) & & \(\left(0.6265\) & \(0.9521\) & \(0.8547\) & \(0.8774\) & \(0.7292\) & \(0.9043\) & \(0.9793\) & \(0.8476\) & \(1.0195\right)^{\text{T}}\) \\ \cline{2-13}  & \(\text{mean}\left(\mathbf{\xi}-\mathbf{\xi}\right)\) & \(1\) & \(\left(0.1940\right.\) & \(-0.0534\) & \(-0.0025\) & \(-0.0679\) & \(0.0779\) & \(-0.0357\) & \(0.0001\) & \(0.0473\) & \(-0.0056\right)^{\text{T}}\) \\ \cline{2-13}  & \(\text{diag}(\hat{P})\) & & \(\left(0.6280\) & \(0.9626\) & \(0.8560\) & \(0.8456\) & \(0.7436\) & \(0.8792\) & \(0.9462\) & \(0.8357\) & \(1.0461\right)^{\text{T}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mean value of the residuals \(\mathbf{\xi}-\mathbf{\xi}\) and the diagonal entries of the covariance matrix \(\hat{P}\) of the residuals evaluated across \(M\) entries of the validation dataset for different \(T_{s}\). As a demonstrative case study, consider a particular subject with vector \(\mathbf{\xi}\) given as  
\[\mathbf{\xi}=\Big{(}0.388\quad 1.137\quad 0.711\quad-0.968\quad-0.482\quad-1.183 \quad 0.430\quad-0.400\quad 1.132\Big{)}^{\mathrm{T}}. \tag{38}\]  
For this subject, the actual coexisting stable steady state is  
\[N_{0}=2.9035\times 10^{5},L_{0}=14.940\times 10^{5},T_{0}=7.6286\times 10^{5}. \tag{39}\]  
Considering the initial conditions and the dose size given by (40) for this subject will result in the state responses \(N(kT_{s}),L(kT_{s}),\ T(kT_{s})\) used for the model personalization. \[N(0)=1\times 10^{5},L(0)=20\times 10^{5},T(0)=50\times 10^{5},\ u(0)=0,\ D=1 \tag{40}\]  
The next step is the parametrization of the state responses. The accuracy of the parametrization is visualized by comparing the original state responses \(N(t),L(t),T(t)\) with their parametric approximations \(\overset{\sim}{N}(t),\overset{\sim}{L}(t),\overset{\sim}{T}(t)\) for \(T_{s}=1/4\) in Figure 4.  
Evaluating vector \(\mathbf{U}\) obtained by parametrizing the state responses by the trained MLP NN according to (20) results in  
\[\mathbf{\xi}=\Big{(}0.5588\quad 1.2151\quad 0.5866\quad-1.0861\quad-0.3160\quad-1.1409 \quad 0.1058\quad-0.3675\quad 1.0203\Big{)}^{\mathrm{T}}. \tag{41}\]  
Figure 3: Comparison of the interval uncertainty of the original parameter vector \(\frac{\pm\Delta\theta}{\mathbf{\theta}}\) and the interval uncertainty of the estimated (personalized) parameter vector \(\frac{\pm\Delta\theta}{\mathbf{\theta}}\).