The intricate structure of the lungs is essential for the gas exchange within the alveolar region. Despite extensive research on the pulmonary vasculature, there are still unresolved questions regarding the connection between capillaries and the vascular tree. A major challenge is obtaining comprehensive experimental data that integrates morphological and physiological aspects. We propose a computational approach that combines data-driven 3D morphological modeling with computational fluid dynamics simulations. This method enables investigating the connectivity of the alveolar capillary network with the vascular tree based on the dynamics of blood flow. We developed 3D sheet-flow models to accurately represent the morphology of the alveolar capillary network and conducted computational fluid dynamics simulations to predict flow velocities and pressure distributions. Our approach focuses on leveraging functional features to identify the most plausible architecture of the system. For given capillary flow velocities and arteriole-to-venule pressure drops, we deduce details about arteriole connectivity. Preliminary connectivity analyses for non-human species indicate that their alveolar capillary network of a single alveolus is linked to at least two arterioles with diameters of 20 μm or a single arteriole with a minimum diameter of 30 μm. Our study provides insights into the structure of the pulmonary microvasculature by evaluating blood flow dynamics. This inverse approach represents a new strategy to exploit the intricate relationship between morphology and physiology, applicable to other tissues and organs. In the future, the availability of experimental data will play a pivotal role in validating and refining the hypotheses analyzed with our computational models.