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 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.

通过深度生成机器学习模型和热力学状态的条件正则化流，我们可以高效地生成整个相图的平衡样本，并在预测固液共存线时降低所需能量评估数量。