Pulmonary embolism (PE) is an acute condition where a blood clot obstructs pulmonary circulation, posing serious health risks, including respiratory failure and sudden death. Chest computed tomography (CT) angiography and functional imaging techniques for perfusion (blood flow) and ventilation (air flow), such as single-photon emission computed tomography, are the gold standards for PE diagnosis, but are costly and involve additional radiation and contrast agents, which can trigger allergic reactions. Alternative diagnostic tools are needed to improve accessibility and safety. CT-derived perfusion and ventilation (CT-P and CT-V) methods quantify pulmonary function from inhale/exhale CT image pairs acquired without contrast. While these physics-based methods are explainable, they are limited by deformable image registration (DIR) algorithm inaccuracies and sensitivity to imaging artifacts. Recent advancements in artificial intelligence (AI) offer solutions to these challenges. Deep learning models can outperform physics-based models in accuracy but are often viewed as black boxes, limiting clinical adoption. In this study, we introduce a novel use of deep learning to predict perfusion and ventilation estimates, while simultaneously incorporating these AI-predictions into the physics-based pipelines in an interpretable way. Our deep learning approach integrates a novel U-Net Transformer architecture modified for Siamese inhale/exhale-CT inputs, utilizing a self-supervised learning strategy to first learn a low-dimensional inhale/exhale-CT representative feature space. We achieve state-of-the-art performance with Spearman correlations 0.70 +/- 0.15 for perfusion and 0.80 +/- 0.06 for ventilation. Moreover, we integrate AI-derived predictions into the CT-P/CT-V pipelines by guiding the DIR algorithm using perfusion/ventilation percentiles to emphasize specific regions. Specifically, we apply weights when solving block matching subproblems within the quadratic penalty DIR algorithm, improving CT-V (67.7% increase) more than CT-P (14.3% increase) estimates, likely due to the additional intricacies of the CT-P method. These findings show the promise of combining AI and physics-based models for more accurate and interpretable pulmonary diagnostics.