# Bayesian inference of composition-dependent phase diagrams

arXiv: https://arxiv.org/abs/2309.01271 · HTML: https://mlsanity.com/paper/2309.01271/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 52 references that are in the map.
- First posted on arXiv 3 Sep 2023.

## Builds on (most cited first, 3 of 3)

- [Stopping criterion for active learning based on deterministic generalization bounds](https://mlsanity.com/paper/2005.07402/) (2020)
- [Stopping Criterion for Active Learning Based on Error Stability](https://mlsanity.com/paper/2104.01836/) (2021)
- [Accurate melting point prediction through autonomous physics-informed learning](https://mlsanity.com/paper/2306.13345/) (2023)

## Built on by (most cited first, 1 of 1)

- [Clarifying the Ti-V Phase Diagram Using First-Principles Calculations and Bayesian Learning](https://mlsanity.com/paper/2506.17719/) (2025)

## Abstract (arXiv)

Phase diagrams serve as a highly informative tool for materials design, encapsulating information about the phases that a material can manifest under specific conditions. In this work, we develop a method in which Bayesian inference is employed to combine thermodynamic data from molecular dynamics (MD), melting point simulations, and phonon calculations, process these data, and yield a temperature-concentration phase diagram. The employed Bayesian framework yields not only the free energies of different phases as functions of temperature and concentration but also the uncertainties of these free energies originating from statistical errors inherent to finite-length MD trajectories. Furthermore, it extrapolates the results of the finite-atom calculations to the infinite-atom limit and facilitates the choice of temperature, chemical potentials, and the number of atoms conducting the next simulation with which will be the most efficient in reducing the uncertainty of the phase diagram. The developed algorithm was successfully tested on two binary systems, Ge-Si and K-Na, in the full range of concentrations and temperatures.