## 2 Methods and Available Data
### Basic Data  
The micro-structure of the Toray-GDL is represented by a stochastic geometry model developed by [PERSON] et al. [37] and analyzed for its transport properties by [PERSON] et al. [9]. The geometry model has three characteristic features:  
* Fiber orientation;
* Binder width;
* Compression. The fiber orientation and binder width are parameters of the [PERSON] model [37], and the compression feature was added by [PERSON] et al. [9]. The micro-structures created by a representation of this model can be characterized as follllows:  
* Porosity;
* Permeability;
* Tortuosity. The porosity is a geometric property, with the permeability and tortuosity being obtained from transport simulations using the LB method. It was shown by [PERSON] et al. [9] that the fiber orientation--represented by stochastic-equivalent ensembles of fiber layers--led to a variation in the permeability and tortuosity. The binder width and compression also affect the transport properties. The geometry model was validated against the real structure using 3D synchrotron data [37]. The consistency of the transport simulations was shown by means of the Karman-Cozeny relationship [9; 13]. Figure 2: Architecture of the CNN representing the proposed ML model. The basic (training) data for the ML model are the image series generated from a stochastic geometry model developed by [PERSON] et al. [37, 38], who specified a fiber model of a Toray 090 GDL based on a stochastic analysis of real fibers and added a binder to fill the void space and achieve the porosity of the real material. Their binder model is represented by a width \(b_{r}\) of binders covering parts of the fibers [37]. Figure 3 illustrates the binder model for selected images. Fibers with a diameter of 7.5 \(\upmu\)m were implemented with an image resolution of 1.5 \(\upmu\)m/px, which was further simplified by representing a fiber layer with five identical images [37]. This simplicity was advantageous for the generation of micro-structures for LB simulations [9, 34] but led to redundancy of the images in the TP direction. This redundancy, in turn, limited the accuracy--on average, by 5.29%--in previous work [39]. [PERSON] used only uncompressed data for training. Although he employed data augmentation--mirroring in two directions and also transposing the images--the accuracy remained limited. Redundant images increase the number of trainable parameters in ML without providing additional information. For this reason, the redundancy of the images was broken by introducing the compression level, as defined by [PERSON] et al. [9]. The introduction of the compression as an additional feature of the data required the specification of the compression level as a second input. Only one number was needed for this purpose. In Figure 2, the second input is shown as a vector of size of 128 intended to match the size of the two inputs of the concatenate layer. This representation was selected to keep the diagram of the architecture as simple as possible, as it is a special extension dedicated to the particular redundancy of the uncompressed input data. The data cited in Figure 3 as A, B, C, and D were reported by [PERSON] et al. [9], uncompressed and compressed. Twenty-five realizations of fiber geometries, multiplied by four different binder distributions, leads to 100 geometries representing the uncompressed material. The image data, representing the realization of a stochastic geometry model, were compressed layer-wise: In regular steps, two adjacent images (representing two adjacent fiber layers) were merged in a binary manner, without creating gray level images. In this way, the total number of images was reduced. On the assumption of the same spatial resolution, the new image series represents the compressed material, as illustrated in detail by [PERSON] et al. [9]. Considering the five steps of compression--10%, 20%, 30%, 40%, and 50%--a total of up to 600 geometries could be available.