## 3 Results and Discussion
### ANN Modeling  
The effect of different levels of osmolality and exposure times on the viability of the selected microorganisms was investigated by using the ANN model. The acquired optimal neural network model demonstrated a good generalization capability for the testing data and could accurately predict the output parameters for the observed input parameters. According to the ANN performance, the optimal number of neurons in the hidden layer for the number of _E. coli_, _L. monocytogenes_, _Salmonella_ spp., Enterobacteriaceaeaee, and TPC was 7 (network MLP 2-7-5), with a focus on achieving the highest value of the coefficient of determination, i.e., R\({}^{2}\) (overall 0.999 for ANN throughout the training period), and the lower values of SOS (Table 4). The ANN performance is defined as the goodness of fit among the experimentally measured, and the model-computed outputs (the sum of R\({}^{2}\) from the measured and calculated number of _E. coli_, _L. monocytogenes_, _Salmonella_ spp., _Enterobacteriaceaee, and TPC) throughout the training steps, the testing, and the validation steps are given in Table 5.  
The obtained weights and biases obtained during ANN modeling are shown in Tables 6 and 7, calculated according to Equation (2). The ANN model was employed to predict the experimental variables, quite satisfactorily, for the observed parameters (as observed in Figure 4, where the experimentally estimated and ANN model-predicted values are displayed). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Network Name**} & \multicolumn{3}{c}{**Performance \({}^{*}\)**} & \multicolumn{3}{c}{**Error \({}^{**}\)**} & \multirow{2}{*}{**Training Algorithm**} & \multirow{2}{*}{**Error Function**} & \multirow{2}{*}{**Hidden Activation**} & \multirow{2}{*}{**Output Activation**} \\ \cline{2-2} \cline{6-9}  & **Train.** & & & & & & & & \\ \hline MLP 2-7-5 & 0.999 & 0.992 & 0.999 & 0.004 & 0.007 & 0.004 & BFGS 222 & SOS & Logistic & Identity \\ \hline \hline \end{tabular}  
* The performance terms describe the coefficients of determination; ** The error terms show a lack of data for the ANN model.  
\end{table} 
Table 4: Artificial neural network model summary (performance and errors). Figure 3: PCA of independent variables and the responses of the microorganisms’ viability. Figure 4 illustrates the experimentally counted and ANN model-predicted values for _E. coli._, _L. monocytogenes_, _Salmonella_ spp., Enterobacteriaceaeae, and TPC, revealing that the ANN model satisfactorily predicted the experimental variables. The Accuracy of the Models and the Residual Analysis  
To numerically verify the coefficient of determination (R\({}^{2}\)) for the accuracy of the displayed model, the reduced chi-square (x\({}^{2}\)), mean bias error (MBE), root mean square error (RMSE), and mean percentage error (MPE) were calculated, as shown Table 8. In addition, the model feature fit was examined, and the residual analysis results are presented in Table 9. \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Cycle**} & \multicolumn{4}{c}{**ANN**} \\ \cline{2-6}  & _E. coli_ & _L. monocytogenes_ & _Salmonella_ spp. & **Enterobacteriaceae** & **TPC** \\ \hline Train & 0.9998 & 0.9969 & 0.9990 & 0.9996 & 0.9995 \\ \hline Test & 0.9889 & 0.9971 & 0.9868 & 0.9936 & 0.9983 \\ \hline Validation & 0.9994 & 0.9992 & 0.9985 & 0.9994 & 0.9998 \\ \hline \end{tabular}
\end{table} 
Table 5: Coefficients of determination between experimentally measured and ANN outputs, during training, testing and validation steps.