Spatio-temporal chaotic dynamics in a two-dimensional excitable medium is (cross-)textlessbrtextgreaterestimated using a machine learning method based on a convolutional neural networktextlessbrtextgreatercombined with a conditional random field. The performance of this approach istextlessbrtextgreaterdemonstrated using the four variables of the Bueno-Orovio-Fenton-Cherry modeltextlessbrtextgreaterdescribing electrical excitation waves in cardiac tissue. Using temporal sequences oftextlessbrtextgreatertwo-dimensional fields representing the values of one or more of the model variablestextlessbrtextgreateras input the network successfully cross-estimates all variables and provides excellenttextlessbrtextgreaterforecasts when applied iteratively.