Boltzmann generators for amorphous particle systems

2026-07-24 · Source: stat.ML updates on arXiv.org · Field: Science & Research — Physical Sciences & Chemistry, Mathematics & Computational Sciences, Artificial Intelligence & Machine Learning · Depth: Expert, extended

Summary

The paper introduces the equivariant Riemannian stochastic interpolant (eRSI) framework for efficiently sampling equilibrium configurations of amorphous materials, such as structural glasses. This novel generative model combines Riemannian stochastic interpolants with equivariant flow matching, rigorously incorporating periodic boundary conditions and the inherent symmetries of multi-component particle systems. The method adapts an equivariant graph neural network to operate directly on the torus, ensuring geometric and symmetry constraints are enforced. Numerical experiments on a 2D binary mixture of metallic glass formers, with system sizes N=10 and N=44 particles at T=0.1, demonstrate eRSI's superior performance. Compared to equivariant flow matching (eFM) and non-equivariant Riemannian stochastic interpolants (RSI), eRSI yields higher-quality generations, faster convergence of physical observables like potential energy and specific heat with fewer samples, and improved scalability, avoiding unphysical particle overlaps seen in eFM.

Key takeaway

For research scientists and machine learning engineers working on simulating complex disordered materials, this work demonstrates that explicitly incorporating geometric and symmetry constraints into generative models is crucial. Your efforts in sampling equilibrium configurations of amorphous systems will be significantly more efficient and accurate by adopting the equivariant Riemannian stochastic interpolant (eRSI) framework. This approach ensures physically plausible outputs and enables reliable, unbiased estimation of thermodynamic averages, which is vital for understanding material properties. Consider integrating eRSI or similar symmetry-aware methods to overcome the limitations of traditional simulation techniques and less constrained generative models.

Key insights

Equivariant Riemannian stochastic interpolants (eRSI) enable efficient, unbiased sampling of amorphous material configurations by enforcing geometric and symmetry constraints.

Principles

• Generative models for physical systems require tractable likelihoods.
• Enforcing geometric and symmetry constraints improves generative performance.
• Riemannian stochastic interpolants are well-suited for periodic boundary conditions.

Method

The eRSI framework extends Riemannian stochastic interpolants by defining G_C-equivariant interpolation functions and adapting an equivariant graph neural network for the torus to learn a G_C-equivariant velocity field.

In practice

• Use eRSI to sample equilibrium configurations of glass-forming liquids.
• Apply importance sampling to generated samples for unbiased observable estimation.
• Adapt GNNs for torus geometry to incorporate periodic boundary conditions.

Topics

• Riemannian Stochastic Interpolants
• Generative Models
• Amorphous Materials
• Graph Neural Networks
• Periodic Boundary Conditions
• Equivariance
• Boltzmann Sampling

Code references

• h2o64/learndiffeq

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.