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We introduce a new approach to reconstruction of the thermodynamic functionsand phase boundaries in two-parametric statistical mechanics systems. Ourmethod is based on expressing the Fisher metric in terms of the posteriordistributions over a space of external parameters and approximating the metricfield by a Hessian of a convex function. We use the proposed approach toaccurately reconstruct the partition functions and phase diagrams of the Isingmodel and the exactly solvable non-equilibrium TASEP without any a prioriknowledge about microscopic rules of the models. We also demonstrate how ourapproach can be used to visualize the latent space of StyleGAN models andevaluate the variability of the generated images.

Counting Phases and Faces Using Bayesian Thermodynamic Integration