AI-driven estimation of partition functions with the PULSE method: Application to the Ising model as a benchmark for the thermodynamic properties of chemically disordered compounds

Predicting the thermodynamic properties of chemically disordered materials is constrained by the combinatorial growth of possible atomic configurations, which makes conventional sampling approaches computationally costly. In this work, we extend the PULSE (Partition function Unsupervised Learning Sampling and Evaluation) approach to the estimation of observable-dependent partition functions, thereby broadening its applicability from local atomic quantities to general thermodynamic observables. This is based on a generative machine-learning approach in which a single model both generates statistically representative atomic configurations and provides explicit partition function estimates. Our primary goal is to assess it on the two-dimensional Ising model, an exactly solvable benchmark system sharing the same statistical-mechanical formulation as chemically disordered binary materials, and compare its performance against exact brute-force calculations as well as Wolff and Wang–Landau Monte Carlo algorithms. PULSE reproduces the relevant partition functions accurately using a limited number of configurations, at a sampling cost that does not grow with system size. These key results demonstrate the relevance of our method to enable the study of disordered materials at scales that are difficult to achieve using conventional approaches, and with limited computational effort.