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