Boltzmann Generators for sampling many-body systems in the isobaric-isothermal ensemble

Abstract

Boltzmann generators (BGs) are exact-likelihood generative models that can be used to sample equilibrium states of many-body systems from the canonical ensemble and to compute the associated Helmholtz free energy. Moreover, they can achieve an immense speed-up with respect to previous methods (i.e., Molecular Dynamics (MD) and Markov Chain Monte Carlo (MCMC)), because they do not need to cross free-energy barriers and can therefore avoid the rare-event problem. However, BGs are not suitable for sampling across phase transitions between phases with positional order, because these phases will generally not be commensurate to the box after the transition. In this work, we present an NPT BG. This unsupervised machine learning model can sample equilibrium states from the isobaric-isothermal ensemble. Furthermore, it could eventually be used to compute the associated Gibbs free energy and to sample across phase transitions. We show that samples generated by this model are in good agreement with samples obtained from MD simulations. Furthermore, we derive an estimate of the Gibbs free energy in terms of samples generated by the NPT BG