## 5 Results
These breaking faces are closer than the minimum domain size (100 in each coordinate direction) for these kinds of LB simulations, as identified by [PERSON] et al. [26]. The inner structure is characterized by the porosity and the relationship \((V_{p}/S_{p})\) which is used in the Kozeny-Carman trend, Equations (4) and (5). The values for \((V_{p}/S_{p})\) in the table are related to the resolution of 1.797 um/px of the original images (see Section 3.2). [PERSON] et al. [41] measured the TP permeability of Toray GDL as 10.9 \(\pm\) 1.2 um\({}^{2}\), which is closer to the results of the LB simulations in artificial structures by [PERSON] et al. [26] than to those from the segmentations of real data in Table 3. This indicates that the image segmentation possibly caused larger errors than the LB ones and the ML predictions. The IP permeability is systematically larger than the TP permeability, which is consistent with systematic investigations into the artificial micro-structures of Toray GDLs [26]. The permeability of series R2 along the compression of the material is depicted in Figure 11. Series R3 is shown in Figure 12.  
[PERSON] et al. [42] measured the IP permeability of three kinds of GDL, one of them being Toray 060, under mechanical compression. They observed a decrease in the IP permeability of Toray GDL by a factor of approximately two under compressions of up to 24%. Their experiments showed variances of only 10-15%. This behavior is consistent with the predicted \(\kappa_{ML}\) values in the IP columns of Table 3 and the corresponding symbols in Figures 11 and 12. The IP permeability and tortuosity were calculated in only one direction--the x coordinate--because the geometry model of [PERSON] et al. [32] was stochastically invariant in the plane. The real data from [PERSON] [35], however, were not invariant in its two IP directions because of the morphological changes of the micro-structure under compression. The x coordinate is the transport direction in the IP simulations. According \begin{table}
\begin{tabular}{l c c c c c c}  & \multicolumn{2}{c}{**TP**} & \multicolumn{2}{c}{**IP**} \\  & \(\kappa\) & \(\tau\) & \(\kappa\cdot\tau\) & \(\kappa\) & \(\tau\) & \(\kappa\cdot\tau\) \\  & \(\mu\)**m\({}^{2}\)** & & \(\mu\)**m\({}^{2}\)** & & & \(\mu\)**m\({}^{2}\)** \\ \hline min & 8.89 & 1.17 & 11.73 & 17.44 & 1.07 & 19.23 \\ max & 11.94 & 1.36 & 15.18 & 19.82 & 1.14 & 22.02 \\ average & 10.54 & 1.27 & 13.43 & 18.83 & 1.10 & 20.80 \\ median & 10.54 & 1.28 & & 18.85 & 1.10 & \\ std. deviation \(\sigma\) & 0.62 & 0.038 & 0.75 & 0.56 & 0.014 & 0.69 \\ variance \(\sigma^{2}\) & 0.38 & \(1.5\times 10^{-3}\) & & 0.32 & \(1.9\times 10^{-4}\) & \\ var. coeff. & \(5.9\times 10^{-2}\) & \(3.0\times 10^{-2}\) & \(5.58\times 10^{-2}\) & \(3.0\times 10^{-2}\) & \(1.3\times 10^{-2}\) & \(3.3\times 10^{-2}\) \\ \hline average (B) in [26] & 11.18 & 1.27 & & 17.98 & 1.11 & \\ average (C) in [26] & 10.51 & 1.29 & & 17.81 & 1.11 & \\ favored: & C & B & B & B, C & \\ \end{tabular}
\end{table} 
Table 2: Tortuosity and permeability of 50 sub-sections of real data of series R1, predicted by the CNN, were trained with fold no. 4. The physical units of the variance are the square of the units in the column headers. The lower section shows the characteristics of the training data. to Figure 6, this direction is across the channel in the mechanical compression setup of [PERSON] [35]. This fact may affect the LB simulations presented in Table 3 and Figure 11.  
The consistency of the predicted data was evaluated via the product \(\kappa\cdot\tau\). According to Equation (4), a constant was fitted to match \(\kappa\cdot\tau\) with \(\varepsilon\cdot\left(V_{p}/S_{p}\right)^{2}\). The latter characterizes the compression of the material, assuming an almost similar shape of the inner structure. Series R3 shows some outliers of \(\left(V_{p}/S_{p}\right)\) in Table 3, namely for compression levels 24%, 28%, and 31%.