Grand Canonical Generators
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.
This article introduces Grand Canonical Generators (GCG), a novel generative framework that extends Boltzmann generators to the grand canonical ensemble, offering new methods for modeling complex systems in statistical mechanics.
What happened
The article introduces Grand Canonical Generators (GCG), a generative framework that extends Boltzmann generators to the grand canonical ensemble. Two designs are presented: one conditions a variable-size generative model on the chemical potential, sampling particle number and configuration jointly. The second design factorizes the grand canonical distribution into a particle-number distribution and a canonical Boltzmann density, allowing the use of existing Boltzmann generators and supporting self-normalized importance sampling. Empirical results demonstrate the effectiveness of GCG in reproducing grand canonical observables in systems like Lennard-Jones fluids and methane adsorption in zeolites.
Why it matters
This development is significant for AI developers and researchers working on generative models for complex systems, as it provides a new framework for modeling systems with variable particle numbers and chemical potentials, enhancing the accuracy and applicability of generative models in statistical mechanics and related fields.
- GCG extends Boltzmann generators to handle variable particle numbers and chemical potentials.
- Two designs are presented, one using variable-size models and the other factorizing the grand canonical distribution.
- The framework supports self-normalized importance sampling and uses existing Boltzmann generators.
- Empirical results show GCG's effectiveness in modeling complex systems.
The bigger picture
GCG has practical implications for modeling complex systems in statistical mechanics, such as Lennard-Jones fluids and methane adsorption in zeolites, by enabling accurate reproduction of grand canonical observables across different chemical potentials.
The article presents Grand Canonical Generators (GCG), a novel framework for generative modeling in the grand canonical ensemble, offering new methods for statistical mechanics and complex system modeling.
Technical details
- Grand Canonical Generators (GCG) extend Boltzmann generators to the grand canonical ensemble.
- The framework includes two designs: one conditions a variable-size generative model on the chemical potential, and the other factorizes the grand canonical distribution into a particle-number distribution and a canonical Boltzmann density.
- The factorized formulation supports self-normalized importance sampling (SNIS) and uses existing Boltzmann generators for the canonical component.
- The model analytically encodes the linear chemical-potential dependence.
FAQ
What is Grand Canonical Generators (GCG)?
GCG is a generative framework that extends Boltzmann generators to the grand canonical ensemble, enabling modeling of systems with variable particle numbers and chemical potentials.
What are the two designs of GCG?
The first design conditions a variable-size generative model on the chemical potential, sampling particle number and configuration jointly. The second design factorizes the grand canonical distribution into a particle-number distribution and a canonical Boltzmann density.
How does GCG support self-normalized importance sampling?
The factorized formulation of GCG allows the use of existing Boltzmann generators and supports self-normalized importance sampling (SNIS), enabling tractable likelihoods.
What systems were used to test GCG?
GCG was tested on systems like Lennard-Jones fluids and methane adsorption in zeolites, demonstrating its ability to reproduce grand canonical observables across different chemical potentials.
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Originally published by arXiv - stat.ML on Oct 2, 2026.
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