Efficient mapping of phase diagrams with conditional Boltzmann Generators

TL;DR

This paper introduces a deep generative model based on conditional Boltzmann Generators that efficiently maps entire phase diagrams, accurately predicting phase boundaries with fewer simulations.

Contribution

It develops a normalizing flow approach conditioned on thermodynamic states to predict phase diagrams from minimal reference data, reducing computational costs.

Findings

Accurately predicts the solid-liquid coexistence line for Lennard-Jones system.

Achieves excellent agreement with traditional free energy methods.

Reduces the number of energy evaluations needed for phase diagram prediction.

Abstract

The accurate prediction of phase diagrams is of central importance for both the fundamental understanding of materials as well as for technological applications in material sciences. However, the computational prediction of the relative stability between phases based on their free energy is a daunting task, as traditional free energy estimators require a large amount of simulation data to obtain uncorrelated equilibrium samples over a grid of thermodynamic states. In this work, we develop deep generative machine learning models based on the Boltzmann Generator approach for entire phase diagrams, employing normalizing flows conditioned on the thermodynamic states, e.g., temperature and pressure, that they map to. By training a single normalizing flow to transform the equilibrium distribution sampled at only one reference thermodynamic state to a wide range of target temperatures and pressures, we can efficiently generate equilibrium samples across the entire phase diagram. Using a permutation-equivariant architecture allows us, thereby, to treat solid and liquid phases on the same footing. We demonstrate our approach by predicting the solid-liquid coexistence line for a Lennard-Jones system in excellent agreement with state-of-the-art free energy methods while significantly reducing the number of energy evaluations needed.