  We introduce a new approach to reconstruction of the thermodynamic functions
and phase boundaries in two-parametric statistical mechanics systems. Our
method is based on expressing the Fisher metric in terms of the posterior
distributions over a space of external parameters and approximating the metric
field by a Hessian of a convex function. We use the proposed approach to
accurately reconstruct the partition functions and phase diagrams of the Ising
model and the exactly solvable non-equilibrium TASEP without any a priori
knowledge about microscopic rules of the models. We also demonstrate how our
approach can be used to visualize the latent space of StyleGAN models and
evaluate the variability of the generated images.
