Mounting evidence shows that Alzheimer's disease (AD) is characterized by the propagation of tau aggregates throughout the brain in a prion-like manner. Since current pathology imaging technologies can only provide a spatial brain mapping of tau accumulation, computational modeling becomes indispensable in analyzing the spatiotemporal propagation patterns of widespread tau aggregates. To address this challenge, we present a novel physics-informed neural network for AD by conceptualizing the intercellular spreading of tau pathology in a reaction-diffusion model, where each node (brain region) is ubiquitously wired with other nodes while interacting with amyloid burdens. In this context, we formulate the biological process of tau spreading in a principled potential energy transport model that describes the mechanistic role of Aβ-tau interaction in the widespread flow of tau aggregates. The physics principle and mathematical insight allow us to develop an explainable neural network to uncover the spatiotemporal dynamics of tau propagation from the unprecedented amount of longitudinal neuroimages. On top of this, we introduce a symbolic regression module to further elucidate the analytic expressions underlying Aβ-tau interaction and tau propagation mechanism. We have achieved not only an enhanced prediction accuracy of tau propagation on ADNI and OASIS datasets but also a system-level understanding of the pathophysiological mechanism in AD progression, suggesting great potential for research in AD and AD-related dementias.