## 1 Introduction
Their micro-structures were generated by placing artifacts of random sizes and positions in the volumetric domain. [PERSON] et al. [22] set out a comprehensive set of descriptors for their characterization of porous materials. Three-dimensional (3D) convolutional neural networks (CNNs) were employed by [PERSON] et al. to characterize material [23], who also investigated [PERSON]'s modulus in their samples and analyzed the transferability of their trained ML model to images of different sizes. [PERSON] et al. [24] not only characterized porous material but also coupled their ML approach with a genetic algorithm for the design optimization of redox flow batteries. Meanwhile, [PERSON] et al. [25] used their ML application as a tool to fill gaps in their membrane database with reliable values. A comprehensive overview of the application of various ML methods to porous material was presented by [PERSON] et al. [26]. Meanwhile, [PERSON] et al. [27] were even able to simulate fluid flow in porous material by means of DL. For fuel cell applications, [PERSON] et al. [28] identified ML as a promising method for optimizing GDL micro-structures. [PERSON] et al. [29] applied DL methods to the analysis of images of the catalyst layer of PEFCs. The micro-structure of solid oxide fuel cells (SOFCs) was also evaluated by [PERSON] et al. [30] using the DL method. Dynamic processes were classified by [PERSON] et al. using time-resolved X-ray tomography [31]. This study investigates the permeability of fiber-based GDLs. The permeabilities of micro-structures generated from a stochastic geometry model were determined in previous LB simulations [9], as depicted in Figure 1. Not only the arrangement of fibers but also the distribution of binders was varied. Furthermore, the underlying micro-structures were compressed. The set of simulation results were then used to train a CNN to predict permeability from the image series. In a similar way, [PERSON] and [PERSON] [32] developed a CNN for the prediction of GDL permeability, with its data generated by pore network modeling (PNM). The relevance of the GDL characteristics as a function of binder and compression was recently analyzed by [PERSON] et al. [33]. Whereas the earlier work of the authors [9; 10; 34] is based on physical modeling, using the LB method, the present study is data-driven: given the raw data--in this case, the micro-structure of a fiber-based GDL--and its characterization (here, permeability), an ML model is developed to predict these characteristics from a given micro-structure, without the need for HPC simulations. This paper is organized on the basis of DL, as proposed by [PERSON] and [PERSON] [35]. The method for generating the training data is described in Section 2, as is the proposed ML model. This includes special features of the data, inherent to the micro-structure, one of which affects the architecture of the CNN. Section 3 presents an overview of the data and their preparation for training. The ML model was validated as shown in Section 4. The predictions of the ML model on real data are presented and discussed in Section 5. Finally, the study is summarized in Section 6.