Problems with a large number of interacting particles are ubiquitous in science and key to many future technologies. Recently, the successful application of deep learning methods to such problems led to remarkable progress in statistical mechanics, quantum chemistry and condensed matter physics. We will investigate variational methods and Graph Neural Networks in the context of many-body physics problems related to the identification of ground states and phases of matter. For supervised methods a crucial aspect will be the data efficiency and the combination with few-shot learning and physics inspired model architectures.