Cardiac electrophysiology (EP) models achieved good progress in simulating cardiac electrical activity. However numerical issues and computational times hamper clinical applicability of such models. Moreover , personalisation can still be challenging and model errors can be difficult to overcome. On the other hand, deep learning methods achieved impressive results but suffer from robustness issues in healthcare due to their lack of physiological knowledge. We propose a novel approach which is based on deep learning in order to replace numerical integration of partial differential equations. This has the advantage to directly learn spatio-temporal correlations, which increases stability. Moreover, once trained, solutions are very fast to compute. We present first results in state estimation based on few measurements and evaluate the forecasting power of the trained network. The proposed method performed very well on this preliminary evaluation. It opens up possibilities towards data-driven personalisation, to overcome model error by learning from the data.