By today, we understand that quantum correlations lie at the heart of quantum physics, and a whole field of research has developed around the understanding and exploitation of quantum correlations. Their characterization is an ongoing effort, with new aspects being revealed every day. The complexity of quantum systems and the counter-intuitive phenomena that arise from it makes this task a formidable one. Recent research ambitions of understanding these effects on networks add an additional layer of complexity, leaving a variety of open problems and unanswered questions.

This thesis contributes to these ongoing efforts with analytic and numerical tools, with a particular focus on exploring the utility of artificial neural networks in this endeavor. In particular, we examine several examples in the prototypical hierarchy of quantum correlations: quantum entanglement, Einstein–Podolsky–Rosen steering, and Bell nonlocality, as well as its extension to networks. We conclude with a summary and an outlook on the field and possible further directions.