发表机构
Institute of Physics, Chinese Academy of Sciences; University of Chinese Academy of Sciences; Gaoling School of Artificial Intelligence, Renmin University of China（中国科学院物理研究所; 中国科学院大学; 中国人民大学高瓴人工智能学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
EP-Flow提出一种基于熵多面体流的无序晶体结构预测方法，无需位点级标注，通过联合生成占据、坐标和晶格参数，在基准上达到最优性能。
AI 中文摘要
生成模型在有序晶体结构预测方面取得了快速进展，然而许多功能材料本质上是无序的，其性质由替代混合、空位或间隙物种控制。现有的晶体生成器要么假设确定性的位点占据，要么需要位点级无序标注，而当化学式作为主要输入时，这些标注往往不可用。我们通过占据分布矩阵（ODM）来表述无序晶体结构预测，这是一种连续的逐位点-逐物种表示，统一了有序晶体、固溶体、空位无序和间隙占据。有效的ODM必须满足耦合的位点占据、质量守恒和非负性约束，将每个样本置于一个依赖于化学式的运输多面体上。我们提出了熵多面体流（EP-Flow），一种边际约束的流匹配框架，将异质多面体规范化到一个共享的双中心空间，学习保持边际的流，并通过Sinkhorn逆映射恢复可行的占据。通过联合生成占据、分数坐标和晶格参数，EP-Flow在源自COD和MPDS的公式条件无序CSP基准上达到了最先进的性能，显著优于改编的有序晶体生成器。分析进一步表明，EP-Flow恢复了稀疏且化学上有意义的局部无序模式，而不仅仅是匹配全局组成统计。
英文摘要
Generative models have made rapid progress in ordered crystal structure prediction, yet many functional materials are intrinsically disordered, with substitutional mixing, vacancies, or interstitial species controlling their properties. Existing crystal generators either assume deterministic site occupations or require site-level disorder annotations, which are often unavailable when the chemical formula is the primary input. We formulate disordered crystal structure prediction through an Occupancy Distribution Matrix (ODM), a continuous site-by-species representation that unifies ordered crystals, solid solutions, vacancy disorder, and interstitial occupancy. A valid ODM must satisfy coupled site-wise occupancy, mass-conservation, and non-negativity constraints, placing each sample on a formula-dependent transportation polytope. We propose Entropic Polytope Flow (EP-Flow), a marginal-constrained flow matching framework that canonicalizes heterogeneous polytopes into a shared double-centered space, learns a marginal-preserving flow, and recovers feasible occupancies through a Sinkhorn inverse map. By jointly generating occupancies, fractional coordinates, and lattice parameters, EP-Flow achieves state-of-the-art performance on formula-conditioned disordered CSP benchmarks derived from COD and MPDS, substantially outperforming adapted ordered-crystal generators. Analyses further show that EP-Flow recovers sparse and chemically meaningful local disorder patterns rather than merely matching global composition statistics.
