  Atomic structures and adatom geometries of surfaces encode information about
the thermodynamics and kinetics of the processes that lead to their formation,
and which can be captured by a generative physical model. Here we develop a
workflow based on a machine learning-based analysis of scanning tunneling
microscopy images to reconstruct the atomic and adatom positions, and a
Bayesian optimization procedure to minimize statistical distance between the
chosen physical models and experimental observations. We optimize the
parameters of a 2- and 3-parameter Ising model describing surface ordering and
use the derived generative model to make predictions across the parameter
space. For concentration dependence, we compare the predicted morphologies at
different adatom concentrations with the dissimilar regions on the sample
surfaces that serendipitously had different adatom concentrations. The proposed
workflow is universal and can be used to reconstruct the thermodynamic models
and associated uncertainties from the experimental observations of materials
microstructures. The code used in the manuscript is available at
https://github.com/saimani5/Adatom_interactions.
