While the potential groundbreaking role of mathematical modeling in electrophysiology has been demon-strated for therapies like cardiac resynchronization or catheter ablation, its extensive use in clinics is pre-vented by the need of an accurate customized conductivity identification. Data assimilation techniques are,in general, used to identify parameters that cannot be measured directly, especially in patient-specific set-tings. Yet, they may be computationally demanding. This conflicts with the clinical timelines and volumesof patients to analyze. In this paper, we adopt a model reduction technique, developed by F. Chinesta andhis collaborators in the last 15 years, called Proper Generalized Decomposition (PGD), to accelerate the esti-mation of the cardiac conductivities required in the modeling of the cardiac electrical dynamics. Specifically,we resort to the Monodomain Inverse Conductivity Problem (MICP) deeply investigated in the literaturein the last five years. We provide a significant proof of concept that PGD is a breakthrough in solvingthe MICP within reasonable timelines. As PGD relies on the offline/online paradigm and does not needany preliminary knowledge of the high-fidelity solution, we show that the PGD online phase estimates theconductivities in real-time for both two-dimensional and three-dimensional cases, including a patient-specificventricle.Read less <