  The vast complexity is a daunting property of generic quantum states that
poses a significant challenge for theoretical treatment, especially in
non-equilibrium setups. Therefore, it is vital to recognize states which are
locally less complex and thus describable with (classical) effective theories.
We use unsupervised learning with autoencoder neural networks to detect the
local complexity of time-evolved states by determining the minimal number of
parameters needed to reproduce local observations. The latter can be used as a
probe of thermalization, to assign the local complexity of density matrices in
open setups and for the reconstruction of underlying Hamiltonian operators. Our
approach is an ideal diagnostics tool for data obtained from (noisy) quantum
simulators because it requires only practically accessible local observations.
