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

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 various origin. Our allows propagating uncertainty finite trajectories to automatically performing with respect simulation parameters. Furthermore, our approach provides way automatic optimal sampling in parameter space on Bayesian optimization approach. We validate methodology by constructing diagrams two model systems, Lennard-Jones soft-core potential, compare results existing works studies coexistence simulations. Finally, construct lithium at temperatures above 300 K pressures below 30 GPa machine-learning potential trained ab initio data. performs well when compared simulations experimental results.