When waves propagate in media with fluctuating index of refraction, they may merge and form branches of high-amplitude intensities in certain random directions. The resulting wave branching is a singular phenomenon that induces some form of coherence through randomness. It may appear in many physical, chemical, and geological and biological systems and has some general features that can be addressed analytically. In quantum physics particles such as electrons have wave-like properties and thus may show similar branching features. Graphene and more generally Dirac solids constitute two dimensional materials where the electronic flow is ultra-relativistic. When a Dirac solid is deposited on a substrate surface with roughness, a local random potential develops through an inhomogeneous charge impurity distribution that affects the charge flow. The result is a chaotic pattern of current branches that develops through focusing and defocusing effects produced by the random surface potential. An additional bias voltage may be used to tune the branching pattern of the currents. Analytical and numerical techniques can be employed in order to investigate the onset and the statistical properties of carrier branches in Dirac solids. We apply machine learning and evaluate the possibility of learning and predicting this statistical phenomenon. We find that methodology similar to that used in chimeras is able to capture the essence of the phenomenon.