Efficient mapping of phase diagrams with conditional Boltzmann Generators
This work addresses the problem of computationally expensive phase diagram prediction for materials science researchers, offering a more efficient method that is incremental in improving existing generative approaches.
The authors tackled the computational challenge of predicting phase diagrams by developing conditional Boltzmann Generators using normalizing flows, which efficiently generate equilibrium samples across thermodynamic states. They demonstrated this by accurately predicting the solid-liquid coexistence line for a Lennard-Jones system, reducing the number of energy evaluations needed compared to state-of-the-art methods.
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.