Motivation: Myocardial $$$T_1$$$ mapping sequences typically require multiple breath-hold scans, leading to limited spatial resolution, patient discomfort and motion artifacts. Moreover, mapping is generally accomplished through three-parameter exponential fitting, which may compromise the accuracy of the estimation due to the model's simplicity. Goal(s): Improve $$$T_1$$$ mapping estimation accuracy, while also reducing acquisition and reconstruction times. Approach: We propose a physics-informed deep learning network to obtain myocardial $$$T_1$$$ maps directly from undersampled k-space following the Extended Phase Graph formulation. Results: Our method is able to estimate $$$T_1$$$ maps for acceleration factors 4 and 8 with minimal error. Impact: We propose a novel physics-based deep learning method that performs accelerated myocardial $$$T_1$$$ mapping directly from undersampled k-space acquisitions considering the Extended Phase Graph formulation, greatly improving the accuracy of the estimated $$$T_1$$$ values while shortening acquisition/reconstruction times.