The mechanical contraction of the pumping heart is driven by electrical excitation waves running across the heart muscle due to the excitable electrophysiology of heart cells. With cardiac arrhythmias these waves turn into stable or chaotic spiral waves (also called rotors) whose observation in the heart is very challenging. While mechanical motion can be measured in 3D using ultrasound, electrical activity can (so far) not be measured directly within the muscle and with limited resolution on the heart surface, only. To bridge the gap between measurable and not measurable quantities we use two approaches from machine learning, echo state networks and convolutional autoencoders, to solve two relevant data modelling tasks in cardiac dynamics: Recovering excitation patterns from noisy, blurred or undersampled observations and reconstructing complex electrical excitation waves from mechanical deformation. For the synthetic data sets used to evaluate both methods we obtained satisfying solutions with echo state networks and good results with convolutional autoencoders, both clearly indicating that the data reconstruction tasks can in principle be solved by means of machine learning.