There is a growing consensus in neuroscience that pathological proteins accumulate and spread along specific large-scale brain networks, indicating the mechanistic role of connectome architecture in the progression of neurodegenerative diseases. Although mounting evidence shows that pathology spreading is a dynamic biological process shaped by the complex interplay between the wiring mechanism of neuronal fibers and the self-organized synchronization of functional fluctuations, current computational methods model the propagation of pathology burden through either structural connectivity (SC) or functional connectivity (FC). To address this limitation, we present a multi-layer transport model to capture the SC/FC-specific propagation of neuropathological burdens and their interactions from longitudinal imaging data. Furthermore, we propose to parameterize the spreading pathways using a physics-informed neural network, enabling the prediction of the progression of pathological events at the baseline. We have evaluated the prediction accuracy of tau aggregates in Alzheimer’s disease (AD), where our method achieves a significantly higher accuracy compared to existing approaches. In addition, the physics principle in our deep model allows us to explore the biological underpinning of how SC-FC interaction contributes to pathology propagation in AD. Taken together, enhanced prediction accuracy and model interpretability suggest the great potential of our deep model in uncovering the pathophysiological mechanism in neurodegenerative diseases through data-driven approaches.