  We consider networks of coupled phase oscillators of different complexity:
Kuramoto-Daido-type networks, generalized Winfree networks, and hypernetworks
with triple interactions. For these setups an inverse problem of reconstruction
of the network connections and of the coupling function from the observations
of the phase dynamics is addressed. We show how a reconstruction based on the
minimization of the squared error can be implemented in all these cases.
Examples include random networks with full disorder both in the connections and
in the coupling functions, as well as networks where the coupling functions are
taken from experimental data of electrochemical oscillators. The method can be
directly applied to asynchronous dynamics of units, while in the case of
synchrony, additional phase resettings are necessary for reconstruction.
