Boltzmann generators for amorphous particle systems
Abstract
Sampling configurations in thermodynamic equilibrium is a long-standing challenge in statistical physics. Boltzmann generators address this problem by employing generative models to propose independent configurations, which are then reweighted via importance sampling using exact likelihood evaluations. Recent Boltzmann generators based on continuous normalizing flows and flow matching have achieved significant success for particle systems and biomolecules. However, these approaches have not been extended to amorphous materials (glasses), for which equilibrium sampling is notoriously slow. Because of their disordered structure, the invariances and geometrical constraints of amorphous materials differ from those of crystals and biomolecules, preventing the direct use of existing generative models. Here, we develop Boltzmann generators tailored to amorphous materials by building the required equivariances directly into Riemannian stochastic interpolants. Our framework incorporates periodic boundary conditions and particle symmetries using equivariant graph neural networks. Numerical experiments demonstrate that enforcing physical symmetries significantly improves the accuracy of Boltzmann generators but also reveal an intrinsic limitation of the continuous-flow formulation: accumulated numerical errors during likelihood integration break time-reversibility, compromising exact thermodynamic reweighting. These results reveal a fundamental challenge for continuous-flow generative models in statistical mechanics and call for alternative approaches that preserve exact thermodynamic consistency.
Related
- Bridging Stochastic Flow Maps and Boltzmann Generators with Normalizing Flows
- Few-Step Boltzmann Generators via Scalable Likelihood Flow Maps
- Mode Coverage in Normalizing Flow Boltzmann Generators via Log-Ratio Variation
- Wave-Particle Decomposition for Kinetic Equations II: Full Boltzmann equation
- Dilation systems with two generators and the optimal Riesz bounds of a basis of ReLU networks
BibTeX
@article{grenioux2026boltzmann,
title = {{Boltzmann generators for amorphous particle systems}},
author = {Louis Grenioux and Leonardo Galliano and Ludovic Berthier and Giulio Biroli and Marylou Gabrié},
journal = {The Journal of Chemical Physics},
year = {2026},
month = oct,
doi = {10.1063/5.0353653},
url = {https://hal.science/hal-05849340v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - JOUR
TI - Boltzmann generators for amorphous particle systems
AU - Louis Grenioux
AU - Leonardo Galliano
AU - Ludovic Berthier
AU - Giulio Biroli
AU - Marylou Gabrié
PY - 2026
DA - 2026/10/28
JO - The Journal of Chemical Physics
DO - 10.1063/5.0353653
UR - https://hal.science/hal-05849340v1
AB - Sampling configurations in thermodynamic equilibrium is a long-standing challenge in statistical physics. Boltzmann generators address this problem by employing generative models to propose independent configurations, which are then reweighted via importance sampling using exact likelihood evaluations. Recent Boltzmann generators based on continuous normalizing flows and flow matching have achieved significant success for particle systems and biomolecules. However, these approaches have not been extended to amorphous materials (glasses), for which equilibrium sampling is notoriously slow. Because of their disordered structure, the invariances and geometrical constraints of amorphous materials differ from those of crystals and biomolecules, preventing the direct use of existing generative models. Here, we develop Boltzmann generators tailored to amorphous materials by building the required equivariances directly into Riemannian stochastic interpolants. Our framework incorporates periodic boundary conditions and particle symmetries using equivariant graph neural networks. Numerical experiments demonstrate that enforcing physical symmetries significantly improves the accuracy of Boltzmann generators but also reveal an intrinsic limitation of the continuous-flow formulation: accumulated numerical errors during likelihood integration break time-reversibility, compromising exact thermodynamic reweighting. These results reveal a fundamental challenge for continuous-flow generative models in statistical mechanics and call for alternative approaches that preserve exact thermodynamic consistency.
SN - 0021-9606
SN - 1089-7690
ER -