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Grand Canonical Generators

arXiv 2610.00683 ↗First posted 30 Sep 2026cs.LG stat.MLcited by 0

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Abstract (arXiv)

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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References · 19

  1. 2022Flow Matching for Generative Modelingcited by 5,702
  2. 2023Equivariant flow matchingcited by 135
  3. 2024Generator Matching: Generative modeling with arbitrary Markov processescited by 86
  4. 2021Normalizing flows for atomic solidscited by 39
  5. 2023Trans-Dimensional Generative Modeling via Jump Diffusion Modelscited by 35
  6. 2020Scalable Normalizing Flows for Permutation Invariant Densitiescited by 22
  7. 2024Neural Thermodynamic Integration: Free Energies from Energy-based Diffusion Modelscited by 14
  8. 2025HIP: Hessian Interatomic Potentials without derivativescited by 12
  9. 2025Scalable Autoregressive 3D Molecule Generationcited by 8
  10. 2025Boltzmann generators for amorphous particle systemscited by 6
  11. 2026Scaling Autoregressive Models for Lattice Thermodynamicscited by 5
  12. 2019Set Flow: A Permutation Invariant Normalizing Flowcited by 4
7 more
  1. 2026Derivative Informed Learning of Exchange-Correlation Functionalscited by 2
  2. 2026Generative Molecular Morphing for Flexible-Size Design via Unbalanced Optimal Transportcited by 2
  3. 2026Few-Step Boltzmann Generators via Scalable Likelihood Flow Mapscited by 2
  4. 2024Grand canonical generative diffusion model for crystalline phases and grain boundariescited by 1
  5. 2025Gradient-based grand canonical optimization enabled by graph neural networks with fractional atomic existencecited by 1
  6. 2026Boltzmann Generators for Condensed Matter via Riemannian Flow Matchingcited by 1
  7. 2026M=oLe-Lambda: Learning the Coupled-Cluster Response State for Energies, Gradients, and Propertiescited by 1

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