## 2 Methods and Data
### Real Data  
The ML model was applied to real data from different sources.  
* One image series of Toray GDL was reconstructed from the BESSY synchrotron, the image source from which the GDL model of [PERSON] et al. [32] was validated. Two images are depicted in Figure 3.
* Two image series were obtained from a Nano CT Zeiss Xradia Versa 420 at the IEK-14 at the Forschungszentrum Julich, allowing a minimal voxel size of 0.5 \(\upmu\)m. [PERSON] [35] investigated Toray TGP-H-060 GDL, one series with labels (Figure 4), and
* one without (Figure 5).  
In 2011, series R1 was obtained from the BESSY synchrotron for validation of the Thiedmann geometry model [32]. The gray level images were segmented into binary BW images, but their quality was not sufficient for LB simulations. Figure 3 shows 2 of the 200 images of dimensions 1250 \(\times\) 1250. The images have a resolution of 1.5 \(\upmu\)m/px. That defines a square section with a side length of 1.875 mm. The porosity of the image stack--calculated by counting pixels--is 0.782.  
The resolution of the images in Figure 3 is the same as in the training data, but the images are larger and are more than 130. This led to the opportunity to randomly select a number of 3D sections of dimensions 130 \(\times\) 512 \(\times\) 512 out of the image stack of 200 \(\times\) 1250 \(\times\) 1250. The resulting permeabilities (TP and IP) predicted by the CNN show a statistical variation, changing with the position of the 3D subset.  
Figure 3: X-ray synchrotron images of dimensions 1250 \(\times\) 1250 from Toray 090 material; (**A**) image no. 56 of 200; (**B**) image no. 163 of 200.  
The difference between Toray 060 and 090 is only the thickness; according to the data sheet, Toray 060 has a thickness of 190 um, whereas Toray 090 has a thickness of 280 um. [PERSON] [35] experimentally analyzed the micro-structure of GDLs of different types, one of them being Toray GDL under compression. Figure 6A displays schematically the membrane electrode assembly (MEA) with a GDL on both sides in the experimental setup of a compression device. The images of the R2 and R3 series were obtained from a Nano CT Zeiss Xradia Versa 420. Figure 6B shows an example.  
GDLs were mechanically compressed by different levels of compression. Series R2 was from the channel side of a punch with a 1.0 mm slit, representing the 1.0 mm channel of a flow field. Series R3 was from the block side, i.e., the flat punch vis-a-vis a punch with a 0.8 mm slit. The images of both the R2 and R3 series spanned a region from one rib across the channel to the other rib in the scheme of Figure 6A. [PERSON] [35] observed that the entire MEA deformed under compression, and therefore affected both GDLs. The GDL on the channel side also intruded into the channel.  
The gray level images were segmented to black/white (BW) ones in order to provide binary micro-structures for the LB simulations as introduced by [PERSON] et al. [26]. The BW images in Figures 4 and 5 display similar segmentation artifacts as those from the X-ray synchrotron in Figure 3. BW images of series R2 and R3 could only be created in thin slices--no more than 40 images per sample--due to the low quality of the images. Because this is too small for robust LB simulations [26], the image packs were stacked one above the other until at least 120 images were achieved. Regarding the transport simulations, an unrealistic periodicity was introduced into the micro-structure. Care must be taken at these inner breaking faces, as they can possibly cause unpredictable side effects. The dimensions of the image series are summarized in Table 1.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Series** & **No.** & **Comp. \%** & **No. of Images** & **Dimensions** \\ \hline R1 & 1 & 0 & 200 & 1250 \(\times\) 1250 \\ \hline R2 & 1 & 6 & 40 & 694 \(\times\) 670 \\  & 2 & 8 & 22 & 671 \(\times\) 688 \\  & 3 & 11 & 27 & 697 \(\times\) 661 \\  & 4 & 13 & 40 &