Patient-specific models of the heart may lead to better understanding of cardiovascular diseases and better planning of therapy. A machine-learning approach to the personalization of an electro-mechanical model of the heart, from the kinematics of the endo- and epicardium, is presented in this paper. We use 4D mathematical currents to encapsulate information about the shape and deformation of the heart. The method is largely insensitive to initialization and does not require on-line simulation of the cardiac function. In this work, we demonstrate the performance of our approach for the joint estimation of three parameters on one heart geometry. We manage to retrieve parameters such that the model matches the 4D observations with an accuracy below the voxel size, in less than three minutes of computation.