Andreas BurgerMalte FrankeLuka MuckoKjell JornerAlan Aspuru-Guzik
Oct 2026
Machine LearningData Science
Abstract
We introduce Grand Canonical Generators (GCG), a generative framework that extends Boltzmann generators to the grand canonical ensemble. We present two designs. The first conditions a variable-size generative model on the chemical potential, sampling particle number and configuration jointly. The second factorizes the grand canonical distribution into a particle-number distribution and the corresponding canonical Boltzmann density. This factorized formulation can use any existing Boltzmann generator for the canonical component, encodes the known linear chemical-potential dependence analytically, and yields a tractable likelihood that supports self-normalized importance sampling (SNIS). Empirically, GCG accurately reproduces grand canonical observables on a Lennard--Jones fluid and methane adsorption in a zeolite, demonstrating generalization across chemical potentials and correction via SNIS and grand canonical Monte Carlo.
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