Functional lung imaging modalities such as hyperpolarized gas MRI ventilation enable visualization and quantification of regional lung ventilation; however, these techniques require specialized equipment and exogenous contrast, limiting clinical adoption. Physiologically-informed techniques to map proton (1H)-MRI ventilation have been proposed. These approaches have demonstrated moderate correlation with hyperpolarized gas MRI. Recently, deep learning (DL) has been used for image synthesis applications, including functional lung image synthesis. Here, we propose a 3D multi-channel convolutional neural network that employs physiologically-informed ventilation mapping and multi-inflation structural1H-MRI to synthesize 3D ventilation surrogates (PhysVENeT). The dataset comprised paired inspiratory and expiratory1H-MRI scans and corresponding hyperpolarized gas MRI scans from 170 participants with various pulmonary pathologies. We performed fivefold cross-validation on 150 of these participants and used 20 participants with a previously unseen pathology (post COVID-19) for external validation. Synthetic ventilation surrogates were evaluated using voxel-wise correlation and structural similarity metrics; the proposed PhysVENeT framework significantly outperformed conventional1H-MRI ventilation mapping and other DL approaches which did not utilize structural imaging and ventilation mapping. PhysVENeT can accurately reflect ventilation defects and exhibits minimal overfitting on external validation data compared to DL approaches that do not integrate physiologically-informed mapping.