We will explore novel aspects of quantum synchronization in networks
of self-sustained oscillators. This includes even-odd effects in the number of levels of the synchronization nodes and the dependence on network topology (number of neighbors and
interaction range). Another interesting direction that we will study is frustration effects and possible
links to frustrated quantum spin systems. Furthermore, we will investigate
symmetry-breaking pattern formation in synchronization networks

Using unsupervised machine-learning schemes, we will investigate phase diagrams of models that exhibit synchronization or other types of long-range order.
We will also explore neural network architectures that involve physical
insights and recent innovations in machine learning to compute steady
states of driven dissipative quantum systems.