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.

翻译：现代生成模型在加速涉及物理系统模拟的多样化任务方面展现出巨大潜力，但必须针对各领域的具体约束进行适配。在生物分子和晶体材料领域已取得显著进展。本文聚焦于非晶态材料（玻璃），即缺乏原子周期性的无序粒子系统。对玻璃形成材料的平衡构型进行采样是一项公认缓慢且困难的任务。通过开发能够生成具有明确定义似然的平衡构型的生成框架，可克服这一障碍。本研究通过利用等变黎曼随机插值框架应对该挑战，该框架结合了黎曼随机插值器与等变流匹配技术。我们的方法严格整合了周期性边界条件与多组分粒子系统的对称性，使等变图神经网络能直接在环面上运算。在模型非晶系统上的数值实验表明，强制几何与对称约束能显著提升生成性能。