Imaging the electrical activity of the heart can be achieved with invasive catheterisation. However, the resulting data are sparse and noisy. Mathematical modelling of cardiac electrophysiology can help the analysis but solving the associated mathematical systems can become unfeasible. It is often computationally demanding, for instance when solving for different patient conditions. We present a new framework to model the dynamics of cardiac electrophysiology at lower cost. It is based on the integration of a low-fidelity physical model and a learning component implemented here via neural networks. The latter acts as a complement to the physical part, and handles all quantities and dynamics that the simplified physical model neglects. We demonstrate that this framework allows us to reproduce the complex dynamics of the transmembrane potential and to correctly identify the relevant physical parameters, even when only partial measurements are available. This combined model-based and data-driven approach could improve cardiac electrophysiological imaging and provide predictive tools.