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.
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Publication details
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- Open access
- Green open access
Cite this article
APA 7
Liu, Q., Wu, L., Li, Q., Peng, Z., Chen, C., Chen, X., Huang, W., & Jin, S. (2026). EP-Flow: Disordered Crystal Structure Prediction without Site-Level Annotations. https://omanscience.com/en/articles/ep-flow-disordered-crystal-structure-prediction-without-site-level-annotations
MLA 9
Liu, Qiuliang, et al. "EP-Flow: Disordered Crystal Structure Prediction without Site-Level Annotations." https://omanscience.com/en/articles/ep-flow-disordered-crystal-structure-prediction-without-site-level-annotations.
Chicago (author–date)
Liu, Qiuliang, Liming Wu, Qi Li, Zhonglong Peng, Chang Chen, Xiaolong Chen, Wenbing Huang, and Shifeng Jin. 2026. "EP-Flow: Disordered Crystal Structure Prediction without Site-Level Annotations." https://omanscience.com/en/articles/ep-flow-disordered-crystal-structure-prediction-without-site-level-annotations.
Harvard
Liu, Q., Wu, L., Li, Q., Peng, Z., Chen, C., Chen, X., Huang, W. and Jin, S. (2026) 'EP-Flow: Disordered Crystal Structure Prediction without Site-Level Annotations', Available at: https://omanscience.com/en/articles/ep-flow-disordered-crystal-structure-prediction-without-site-level-annotations.
Vancouver
Liu Q, Wu L, Li Q, Peng Z, Chen C, Chen X, et al. EP-Flow: Disordered Crystal Structure Prediction without Site-Level Annotations. https://omanscience.com/en/articles/ep-flow-disordered-crystal-structure-prediction-without-site-level-annotations
IEEE
Q. Liu, L. Wu, Q. Li, Z. Peng, C. Chen, X. Chen, W. Huang, and S. Jin, "EP-Flow: Disordered Crystal Structure Prediction without Site-Level Annotations," https://omanscience.com/en/articles/ep-flow-disordered-crystal-structure-prediction-without-site-level-annotations.