Counting Phases and Faces Using Bayesian Thermodynamic Integration

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.