The ECGI inverse problem is still a common area of research. Since the results in the state of the art are not yet satisfactory, exploring new methods for the resolution of the inverse problem of electrocardiography is the main goal of this paper. To this purpose, we suggest to use temporal and spatial constraints to solve the inverse problem using neural networks methods. First, we use a time-delay neural network initialized with the spatial adjacency operator of the heart surface mesh. Then, we suggest a new approach to reconstruct the heart surface potential from the body surface potential using a spatial adaptation of time delay neural network. It consists on taking into account temporal and spatial dependence between potential measures. This allows to exploit the local and dynamic potential propagation properties. We test these approaches on simulated data. Results show that the new approach outperforms the classic time-delay neural network and has considerable improvements with respect to the state-of-the-art methods.