  We present three different neural network algorithms to calculate
thermodynamic properties as well as dynamic correlation functions at finite
temperatures for quantum lattice models. The first method is based on
purification, which allows for the exact calculation of the operator trace. The
second one is based on a sampling of the trace using minimally entangled
states, whereas the third one makes use of quantum typicality. In the latter
case, we approximate a typical infinite-temperature state by wave functions
which are given by a product of a projected pair and a neural network part and
evolve this typical state in imaginary time.
