  The emergence of scanning probe and electron beam imaging techniques have
allowed quantitative studies of atomic structure and minute details of
electronic and vibrational structure on the level of individual atomic units.
These microscopic descriptors in turn can be associated with the local symmetry
breaking phenomena, representing stochastic manifestation of underpinning
generative physical model. Here, we explore the reconstruction of exchange
integrals in the Hamiltonian for the lattice model with two competing
interactions from the observations of the microscopic degrees of freedom and
establish the uncertainties and reliability of such analysis in a broad
parameter-temperature space. As an ancillary task, we develop a machine
learning approach based on histogram clustering to predict phase diagrams
efficiently using a reduced descriptor space. We further demonstrate that
reconstruction is possible well above the phase transition and in the regions
of the parameter space when the macroscopic ground state of the system is
poorly defined due to frustrated interactions. This suggests that this approach
can be applied to the traditionally complex problems of condensed matter
physics such as ferroelectric relaxors and morphotropic phase boundary systems,
spin and cluster glasses, quantum systems once the local descriptors linked to
the relevant physical behaviors are known.
