## 5 Results and Discussion  
The results of the ML model were evaluated according to several parameters. The accuracy of the prediction permeability of the training and validation data by the trained CNN is first presented. As described in Section 3, the ML model was trained on a series of 65 images with 512 \(\times\) 512 dimensions. These were compressed in the through-plane direction in order to cover both uncompressed and compressed images. In the uncompressed format, these images represent a structure sized 130 \(\times\) 512 \(\times\) 512. The prediction of the permeability of the Toray 090 data introduced in Section 2.3 represents the foreseen application of the proposed CNN: a series of images of fixed size, and the same image resolution of 1.5 \(\upmu\)m/px. The accuracy of the predictions shown in Table 2 is below 5.11% in all cases, and in the percentile range for the relevant cases with a binder with \(b_{r}<\) 30 \(\upmu\)m. This is superior to many of the experimental data, as reported by [PERSON] et al. [42]. It is also within the accuracy of LB simulations, given that such simple coarse grids represent the micro-structure [9; 34]. The CNN was trained to make predictions based on micro-structures and their respective compression levels. As noted in Section 2.3, there is a hidden feature--the binder model--embedded in the micro-structure. Without preference for any fold of the cross-validation introduced in Section 4, the last one (No. 5) was selected for further analysis. Although the MSE (Equation (1)) was specified as a loss function for the CNN training, the MPE (Equation (2)) is more convenient for addressing the theoretical viewpoint. Table 2 displays the predicted permeability that was averaged over subsets of particular compression levels and binder widths \(b_{r}\). Moreover, the averaged MPE and MSE are given. The MPE was not homogeneously distributed with respect to the features binder width \(b_{r}\) and compression level. In Table 2, the influence of the features is depicted by the quantiles of permeability, which are dramatically reduced with increasing compression. This effect can be observed for every binder width \(b_{r}\). A reduction in the permeability with increasing binder width \(b_{r}\) of the binder model can also be observed in Table 2. In this case, the permeabilities of the selected compression levels were compared together with the binder width. In comparison to the compression level, the impact of the binder width is less pronounced. The number of data points--less than or equal to 25--is given for each combination of compression level and binder width. Numbers of less than 25 indicate numerical deficits in the previous LB simulations that were already noticed in earlier investigations [9]. This effect tends to emerge at high compression levels and extreme binder widths \(b_{r}=\infty\). The highest compression level of 50% generally has a low level of accuracy in terms of prediction by the CNN. On the one hand, this is the worst-case scenario of the simplified compression algorithm developed earlier [9]. On the other hand,  
Figure 6: Development of the MSE during training. it was found that paper-type GDLs are usually compressed by up to 30% when they are assembled in a fuel cell stack. [PERSON] et al. [1] compressed their GDLs by up to 30%, whereas [PERSON] et al. [43] investigated compressions of up to 40%. The interquartile range (IQR) is the difference between the 75% and 25% quantiles, also known as the third and first quartiles. The IQR is larger than 1 um\({}^{2}\) in most cases but larger than 0.5 um\({}^{2}\) in cases of low permeability, i.e., with medians smaller than 10 um\({}^{2}\). This applies to at least the relevant compression levels of up to 30%. The variation in the permeability caused by the micro-structure--indicated by the IQR--is larger than the MPE presented in Table 2.  
The large variation in the permeability within one group (binder with compression) shown in Table 2 represents the inhomogeneity of the porous material.