## 5 Results  
The CNN was trained separately with permeability \(\kappa\) and tortuosity \(10\cdot\tau\) to achieve models to predict permeability and tortuosity. A training with \(\tau\) was not successful, which demonstrates the dependency of the method from the absolute range of the characteristics. The accuracy of the predicted permeability and tortuosity is shown in Figure 10. The diagrams contain the values of the uncompressed data of fold no. 4. The predictions were obtained using separated CNN weights for permeability and tortuosity, TP and IP. Figure 9: Three layers of the CNN during the prediction of an image stack. The images are not to scale. The symbols in Figure 10a-c are close to the ideal line, representing a good agreement between the predicted data and labeled data. The effect of the binder type on the permeability and TP tortuosity, which was not explicitly trained, is represented by the predicted values; the information is inherent in the trained data. The scale of Figure 10d is different from Figure 10b, because the IP tortuosity varies in a closer range than the TP tortuosity. This is in agreement with the original data calculated by LB simulations by [PERSON] et al. [26]. The real data of Toray GDL consist of 50 sub-regions randomly cut out of the image stack of series R1, and two series R2 and R3 taken from a channel/rib assembly. The predicted data for the cut-outs of series R1 are summarized in Table 2. The product of the permeability \(\kappa\) and tortuosity \(\tau\) will be used later in this section in comparison with series R2 and R3. In Table 2, the min/max values of the product \(\kappa\cdot\tau\) are different from the product of the separate min/max values of \(\kappa\) and \(\tau\), because low values for the tortuosity typically correspond to high values for the permeability and vice versa. The average values in Table 2 are close to the medians for all features. This confirms the absence of skewness in the distributions that could occur in the systematic selection of the positions from where the sub-sections were cut out of the R1 image stack. The average values of the predicted TP and IP permeabilities and tortuosities are compared with the previously published [26] values, separated according to the inherent binder model as introduced in Figure 2. The predicted values best fit to the published values of binder models B and C, representing binder widths of 18 \(\upmu\)m and 30 \(\upmu\)m. The statistical spread can be expressed by the dimensionless variation coefficient \(V=\sigma/\bar{x}\), \(\sigma\) being the standard deviation and \(\bar{x}\) the average value. The variation coefficient of the permeability (TP and IP) is smaller than that of the training data  
Figure 10: Accuracy of the predicted permeability \(\kappa\) and tortuosity \(\tau\) for different binder widths \(b_{r}\), uncompressed; (**a**) TP \(\kappa\); (**b**) IP \(\kappa\); (**c**) TP \(\tau\); and (**d**) IP \(\tau\). as published in [26]. The variation coefficient of the predicted tortuosities is close to that of the predicted permeabilities. Within the training data, it was somewhat smaller. The binder widths in variants A and D were extreme values in the original development of the underlying binder model by [PERSON] et al. [40]. Manual measurements of the binder width in the BW images as shown in Figure 3 are hardly representative because of significant imaging errors. These imaging errors also inhibited a successful LB simulation of this micro-structure. In series R2, the GDL was embedded in an assembly with a 1.0 mm channel width and a 0.8 mm channel width in series R3. The resolution of the images--1.797 um/px--was adapted to the resolution of the training data in the pre-processing step (1.5 um/px). Table 3 summarizes the predicted permeability. The LB simulations in the IP direction did not converge on meaningful physical values. It is believed that the tight stacking of the images led to significant errors at the artificial inner breaking faces.