Fiber-reinforced polymer composites can be manufactured using a process such as Liquid Composite Molding (LCM). For LCM process simulation, material properties such as permeability are required to describe the impregnation behavior of the fiber structure. Determining permeability necessitates modeling of flow behavior of a liquid polymer through the fiber structures over several spatial scales ranging from micrometers (microscale) to millimeters (mesoscale) to meters (macroscale). To speed up the multiscale simulation workflow, it is desirable to replace the permeability estimation step in one or more of the spatial scales with machine learning-based surrogate models or emulators. A comprehensive dataset [1] of fibrous microstructures and their numerically computed permeabilities was generated using the commercial solver GeoDict for the task of supervised learning. In our previous work [2], we developed feature-based and geometry-based emulators, using fully connected neural networks and 3D convolutional neural networks, for predicting the principal permeabilities of 3D fibrous microstructures with the best relative error of 8.33%. In this work, we further improved the performances of our geometry-based emulators using physics-based data augmentation techniques and using components from recent vision-based deep learning architectures such as transformer blocks. These trained emulators for microscale permeability prediction are then employed in a two-scale simulation workflow to estimate the flow behavior in the higher spatial scale, i.e., flow between the fiber bundles in stacked textile layers (mesoscale). In this work, the mesoscale permeabilities estimated by a conventional two-step simulation workflow is compared against our novel scale-bridging workflows, where the microscale permeability estimation step is replaced by either feature-based or geometry-based emulators. Such scale-bridging workflows lead to faster inference times compared to a two-step simulation workflow, at the cost of accuracy. References: [1] T. Schmidt, S. Cassola, M. Duhovic, and D. May, “Numerically predicted permeability of over 6500 artificially generated fibrous microstructures.” Zenodo, Oct. 27, 2023. doi: 10.5281/zenodo.10047095. [2] D. K. Natarajan et al., “Data-driven permeability prediction of 3D fibrous microstructures,” Proceedings of ECCOMAS Congress 2024 - 9th European Congress on Computational Methods in Applied Sciences and Engineering, Sep. 2024.