We investigate how simulation specific (physical) constraints can be incorporated into a large family of machine learning methods that contains, for example, (hierarchical) kernel-based methods and deep neural networks. These constraints can either be hard, that is, they can be rigorously guaranteed before the learning process, or soft in the sense that constraint violations are penalized during the training phase. Our research goals comprise the identification of constraints that fit well to certain members of the family, a better understanding of the learning process, and steering the learning process towards better solutions. For the latter two goals, novel visualization techniques that make it possible to derive new hypotheses about the highly complex learning process will be developed. In turn, these new hypotheses can further refine the visualization techniques, so that an interplay between visualization and better understanding occurs. At the end, the collected insights will be used to develop new visualization techniques that help non-experts to better understand and control the learning process. Examples of considered physical systems will be chosen in close collaboration with PN 1-5.