Boltzmann generators for amorphous particle systems
stat.ML, cond-mat.stat-mech, cs.LG, physics.comp-ph
Submitted: 2025-12-18
Updated: 2026-09-18
Comments: 30 pages, 10 figures. V2 considerably expands the results compared to v1. V3 accepted for publications in J. Chem. Phys
License: http://creativecommons.org/licenses/by/4.0/
The gist: Sampling configurations in thermodynamic equilibrium is a long-standing challenge in statistical physics.
Terminology
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.
Sources
- Solving Statistical Mechanics Using Variational Autoregressive Networks
- FALCON: Few-step Accurate Likelihoods for Continuous Flows
- A Generative Diffusion Model for Amorphous Materials
- Neural Ordinary Differential Equations
- Riemannian Neural Geodesic Interpolant
- Equivariant Flows: sampling configurations for multi-body systems with symmetric energies
- Asymptotically unbiased estimation of physical observables with neural samplers
- Numerical investigation of the equilibrium Kauzmann transition in a two-dimensional atomistic glass
- Diffusion-based Annealed Boltzmann Generators : benefits, pitfalls and hopes
- Performance of machine-learning-assisted Monte Carlo in sampling from simple statistical physics models
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