Riemannian Stochastic Interpolants for Amorphous Particle Systems

TL;DR

This paper introduces a Riemannian stochastic interpolation method for generating equilibrium configurations of amorphous materials, leveraging symmetry-aware neural networks to improve sampling efficiency and accuracy.

Contribution

It develops an equivariant Riemannian stochastic interpolation framework tailored for amorphous particle systems, addressing the challenge of sampling disordered materials.

Findings

Enhanced generative performance with symmetry constraints

Effective incorporation of periodic boundary conditions

Improved sampling of amorphous systems

Abstract

Modern generative models hold great promise for accelerating diverse tasks involving the simulation of physical systems, but they must be adapted to the specific constraints of each domain. Significant progress has been made for biomolecules and crystalline materials. Here, we address amorphous materials (glasses), which are disordered particle systems lacking atomic periodicity. Sampling equilibrium configurations of glass-forming materials is a notoriously slow and difficult task. This obstacle could be overcome by developing a generative framework capable of producing equilibrium configurations with well-defined likelihoods. In this work, we address this challenge by leveraging an equivariant Riemannian stochastic interpolation framework which combines Riemannian stochastic interpolant and equivariant flow matching. Our method rigorously incorporates periodic boundary conditions and the symmetries of multi-component particle systems, adapting an equivariant graph neural network to operate directly on the torus. Our numerical experiments on model amorphous systems demonstrate that enforcing geometric and symmetry constraints significantly improves generative performance.