Bayesian learning of thermodynamic integration and numerical convergence for accurate phase diagrams

TL;DR

This paper introduces a Bayesian Gaussian process regression framework for accurately reconstructing free energy functions and phase diagrams from molecular dynamics data, with automatic convergence and optimal sampling capabilities.

Contribution

It presents a novel Bayesian approach that propagates uncertainty, automates convergence, and optimizes sampling in phase diagram calculations from molecular dynamics data.

Findings

Successfully reconstructed phase diagrams for Lennard-Jones and soft-core systems.

Achieved accurate lithium phase diagram matching experimental data.

Demonstrated automatic convergence and optimal sampling in simulations.

Abstract

Accurate phase diagram calculation from molecular dynamics requires systematic treatment and convergence of statistical averages. In this work we propose a Gaussian process regression based framework for reconstructing the free energy functions using data of various origin. Our framework allows for propagating statistical uncertainty from finite molecular dynamics trajectories to the phase diagram and automatically performing convergence with respect to simulation parameters. Furthermore, our approach provides a way for automatic optimal sampling in the simulation parameter space based on Bayesian optimization approach. We validate our methodology by constructing phase diagrams of two model systems, the Lennard-Jones and soft-core potential, and compare the results with existing works studies and our coexistence simulations. Finally, we construct the phase diagram of lithium at temperatures above 300 K and pressures below 30 GPa from a machine-learning potential trained on ab initio data. Our approach performs well when compared to coexistence simulations and experimental results.