## 2 Materials and Methods
### Artificial Neural Network
#### 2.4.3 Generating the Training Dataset  
The dataset for training of the MLP NN was generated according to the procedure described as follows. The parameters given by (3) corresponding to virtual oncology subjects were generated randomly while considering their statistical distribution as defined before. The relative interval of parametric uncertainties of the individual model parameters was chosen as  
\[\frac{\Delta\mathbf{\theta}}{\overline{\mathbf{\theta}}}=\Big{(}0.8\quad 0.05\quad 0.05 \quad 0\quad 0.4\quad 0.8\quad 0\quad 0\quad 0\quad 0.25\quad 0.85\quad 0.25 \quad 0.25\Big{)}^{\text{T}}. \tag{21}\]  
Notice that in (21), only \(m=9\) of a total of 14 parameters in the parameter vector \(\mathbf{\theta}\) are considered uncertain, while the others remain nominal, i.e., fixed across the population. In particular, parameters \(a,b,c,\mu,\alpha_{1},\omega,k_{N},k_{L},k_{T}\) are considered uncertain and vary among the subjects. This choice is strongly supported by analyzing the magnitudes and the linear dependencies of the corresponding sensitivity functions of the state variables with respect to the parameters as presented in Appendix A. The sensitivity analysis allowed us to understand the percentual changes in which parameters have an observable effect on the state variables. Then, we could adjust the relative interval parametric uncertainties (21) according to the magnitudes of the sensitivities (see Figures A1-A3) to ensure that their effects are realistically balanced. It means that if the state sensitivity to the \(i\)-th parameter is relatively low, the corresponding parametric uncertainty should be higher than that of a parameter with much greater sensitivity. However, it is important to acknowledge that the uncertainties given by (21) were chosen without the support of clinical results or data, as these are not available in the literature or in the public domain. Experimentally determining the actual statistical distribution of the parameters is beyond the scope of this paper, as it requires large studies with real subjects. Considering the \(1-\alpha=0.95\) confidence level, the entries of matrix \(R\) were determined according to (13) as  
\[R=0.1531\times \begin{pmatrix}0.8&0&0&0&0&0&0&0&0\\ 0&0.05&0&0&0&0&0&0&0\\ 0&0&0.05&0&0&0&0&0&0\\ 0&0&0&0&0&0&0&0&0\\ 0&0&0&0&0&0&0&0&0\\ 0&0&0&0.4&0&0&0&0&0\\ 0&0&0&0&0.8&0&0&0&0\\ 0&0&0&0&0&0&0&0&0\\ 0&0&0&0&0&0&0&0&0\\ 0&0&0&0&0&0.25&0&0&0\\ 0&0&0&0&0&0&0.85&0&0\\ 0&0&0&0&0&0&0&0.25&0\\ 0&0&0&0&0&0&0&0.25\end{pmatrix} . \tag{22}\]  
The structure of matrix \(R\) implies that the covariance matrix \(Q\) defined by (9) will be diagonal, which means that the random variations in the model parameters are not mutually correlated within the population. To create the training dataset, there will be generated a total of 1500 different virtual patients. More specifically, for each of these subjects in the virtual population, a random vector \(\xi\) will be generated considering standard normal distribution (zero mean and unit covariance matrix). The corresponding parameter vector \(\theta\) will be calculated according to formula (8), considering the mean \(\overline{\theta}\) given by the values in Table 1 and matrix \(R\) given by (22). After that, the states of each virtual patient will be simulated by numerically solving the differential Equation (1) using the Runge-Kutta 4-th order numerical integration method [51] to obtain the sampled state responses \(N(kT_{s}),L(kT_{s}),\ T(kT_{s})\) for a given \(T_{s}\) and the dosing period (cycle duration) \(T_{D}\). This simulation (numerical solution) will be repeated for 100 different initial conditions and leading dose sizes \(D\). The initial conditions \(N(0),L(0),\ T(0)\) will also be randomly generated, assuming the normal distributions with the mean values equal to the corresponding stable equilibrium states \(N_{0},L_{0},T_{0}\) and the standard deviations are given as \(\frac{N_{0}}{2},\frac{L_{0}}{2},\frac{T_{0}}{2}\), respectively.