Disordered crystal prediction model works without detailed site labels
EP-Flow: Disordered Crystal Structure Prediction without Site-Level Annotations
Machine Learning
Summary
Predicting the atomic structure of materials that have mixed or missing atoms is hard because usually detailed information about each atomic position is needed. The authors developed a new mathematical way to represent these messy materials using a continuous matrix called an occupancy distribution matrix (ODM). Their new method, EP-Flow, uses advanced flow-based modeling and special constraints to generate realistic crystal structures from just the overall chemical formula. This approach works better than previous models that needed more detailed inputs and can find meaningful patterns of disorder in materials.
What this means in practice
- •For materials engineering teams: Generate detailed atomic arrangements of disordered materials from chemical formulas to inform materials design and property prediction.
- •For computational chemistry software developers: Incorporate occupancy distribution-based generative models to improve predictions of complex crystal structures lacking site-level disorder labels.
Authors
Qiuliang Liu, Liming Wu, Qi Li, Zhonglong Peng, Chang Chen, Xiaolong Chen, Wenbing Huang, Shifeng Jin
Abstract
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.