Counting Phases and Faces Using Bayesian Thermodynamic Integration

TL;DR

This paper presents a novel Bayesian thermodynamic integration method for reconstructing phase diagrams and thermodynamic functions in statistical mechanics models, enabling accurate analysis without prior microscopic knowledge.

Contribution

The authors introduce a Bayesian approach that expresses the Fisher metric via posterior distributions and approximates it with a Hessian, applicable to phase boundary reconstruction and latent space visualization.

Findings

Successfully reconstructed phase diagrams of the Ising model and TASEP.

Accurately visualized StyleGAN latent spaces.

Demonstrated no need for prior microscopic rules.

Abstract

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.