Riemannian Stochastic Interpolants for Amorphous Particle Systems
This work addresses the problem of accelerating simulations for amorphous particle systems, which is incremental as it adapts existing generative models to a specific domain.
The paper tackled the slow and difficult task of sampling equilibrium configurations of amorphous materials (glasses) by developing a generative framework using an equivariant Riemannian stochastic interpolation method, which demonstrated significantly improved generative performance in numerical experiments on model systems.
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.