Riemannian Stochastic Interpolants for Amorphous Particle Systems

2025-12-18

AI Summary

Amorphous materials (e.g., glasses) lack translational periodicity, rendering conventional sampling methods inefficient and unable to reliably sample thermodynamically equilibrium configurations with correct Boltzmann probabilities. Method: We propose the first generative modeling framework rigorously incorporating periodic boundary conditions and multi-component particle symmetry. Our approach innovatively combines stochastic interpolation on Riemannian manifolds with equivariant flow matching, yielding an equivariant graph neural network that operates directly on the torus and explicitly encodes translational, permutation, and compositional invariances. Results: Evaluated across multiple amorphous model systems, our method achieves significantly higher-quality configurations and more accurate likelihood estimation. Sampling efficiency improves by one to two orders of magnitude over molecular dynamics and existing generative models. This work establishes a new paradigm for differentiable, interpretable, and high-fidelity modeling of disordered materials.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Generative Adversarial Networks (GANs) for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

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.

Problem

• Generates equilibrium configurations for amorphous materials
• Overcomes slow sampling in disordered particle systems
• Incorporates periodic boundaries and symmetry constraints

Innovation

• Equivariant Riemannian stochastic interpolation framework
• Incorporates periodic boundary conditions and symmetries
• Uses equivariant graph neural network on torus