Title: Riemannian Stochastic Interpolants for Amorphous Particle Systems
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
Keywords: Generative Modelling, Equivariant Deep Learning, Sampling, Machine Learning for Physics, Stochastic Interpolants, Flow Matchings

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.

TL;DR: We combine equivariant flow matching and Riemannian stochastic interpolants to learn the equilibrium distribution of amorphous particle systems and show that we can reweight the generated samples effectively.