Grand Canonical Generators

2026-09-30

AI Summary

This study addresses the challenge that traditional generative models face in sampling grand canonical ensembles with variable particle numbers. We propose the GCG framework, which extends Boltzmann generators to the grand canonical ensemble, enabling joint or factorized sampling of particle number and configuration. Methodologically, the chemical potential is introduced as a conditioning variable to analytically encode its linear dependence, integrated with variable-length generative models, Boltzmann density decomposition, and a self-normalized importance sampling (SNIS) algorithm to support efficient unbiased correction. Experiments demonstrate that this framework accurately reproduces thermodynamic observables in Lennard-Jones fluids and zeolite adsorption systems, while exhibiting excellent generalization capability across varying chemical potentials.

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.

Problem

• Grand Canonical Ensemble
• Boltzmann Generators
• Generative Models
• Variable Particle Number
• Importance Sampling

Innovation

• Grand Canonical Generators
• Boltzmann generators
• Self-normalized importance sampling
• Variable-size generative model
• Distribution factorization