## 5 Results and Discussion
An increasing width \(b_{r}\) of the binder (Figure 3) increases the local areas blocking the fluid flow through the micro-structure. The inhomogeneity of the fluid flow is illustrated in Figure 4. The permeability decreases under compression in accordance with the Karman-Cozeny relationship [9]. Figure 7 displays the accuracy of the permeabilities predicted by the CNN on the training and validation data, separated by the compression level. The predicted values (the y-axis in the diagrams) are compared with the correct values previously calculated using LB simulations. In addition, the values are colored according to the binder model. Although this feature was not entered into the CNN, the clusters are represented by the ML model, as they were already previously identified by [PERSON] et al. [9]. Along with higher grades of compression, the permeabilities decrease, which is in accordance with [PERSON] et al. [13], our previous investigations [9], and the experimental results of [PERSON] et al. [44] and [PERSON] [45]. As proposed by [PERSON] et al. [9], the compressed data exhibit systematically lower permeabilities than the uncompressed data. Nevertheless, [PERSON] et al. [9] state that the binder model with \(b_{r}=18\) um is the most realistic one  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \(b_{r}\) & **Comp. ** & **No. ** & \multicolumn{3}{c}{**Quantiles of Predicted Permeability/um\({}^{2}\)**} & \multicolumn{3}{c}{**MPE/\%**} & \multicolumn{3}{c}{**MSE/um\({}^{4}\)**} \\ \(\mu\)**m** & **/\%** & & **min** & **25\%** & **50\%** & **75\%** & **Max** & **Training** & **Validation** & **Training** & **Validation** \\ \hline
6 & 0 & 25 & 10.42 & 11.04 & 11.55 & 12.17 & 13.23 & 0.88 & 0.92 & 0.024 & 0.016 \\  & 10 & 25 & 8.62 & 9.20 & 9.56 & 10.14 & 11.19 & 0.73 & 2.77 & 0.007 & 0.077  
compared with the real material. In particular, the high compression level of 50% exhibits a lower degree of accuracy than the others. On the other hand, the high compression levels suffer from inaccuracies as a result of how they were constructed. The most inaccurate data, with 50% compression, were also found to be unrealistic in previous investigations [9]. Figure 8 shows the accuracy of the CNN predictions applied to the validation data, colored according to the binder model. The diagram illustrates that the prediction by the CNN is best for the binder models with \(b_{r}\leq 30\) um, which are more realistic than the other two variants [9]. The parameter \(b_{r}\) for the binder width was originally introduced by [PERSON] et al. [38] to model the distribution of the binder along the fibers of the GDL. They presented variant \(b_{r}=\infty\) as an extreme case. This is illustrated in Figure 3D, in which polygons built by fibers were fully filled with binder material. Due to the stochastic nature of the fiber arrangement, such areas can be large, as in Figure 5D. In these cases, the gas flow would be dramatically inhibited, causing a different flow behavior than in micro-structures with limited binder widths. Figure 8: Predictions on the out-of-sample data; coloring according to the binder model: (A) \(b_{r}=6\) μm; (B) \(b_{r}=18\) μm; (C) \(b_{r}=30\) μm; (D) \(b_{r}=\infty\). Figure 7: Predictions on the training and validation data, colored according to the binder width \(b_{r}\); see Figure 3; (**a**) uncompressed; (**b**) 10% compression; (**c**) 20% compression; (**d**) 30% compression; (**e**) 40% compression; (**f**) 50% compression. The quantiles shown in Table 2 and the deviations of the predicted permeability from the LB simulations presented in Figures 7 and 8 indicate that the accuracy of the predictions of the CNN is smaller than the variation of the permeability caused by the stochastic geometry model. As noted in Section 2.4, only 541 simulations of the 600 available data-sets led to a physically consistent result. The permeabilities of the micro-structures of the other 59 virtual geometries were predicted by the ML model.