EP-Flow: Disordered Crystal Structure Prediction without Site-Level Annotations

2026-10-01

AI Summary

This study addresses the challenge of disordered crystal structure prediction, which is hindered by the absence of site-level annotations and the reliance of existing generative models on deterministic occupancy assumptions. To overcome these limitations, this work proposes an entropy polytope flow matching framework based on occupancy distribution matrices. By introducing a continuous occupancy representation mapped into a shared latent space, the method employs Sinkhorn inverse mapping and marginal constraint optimization to jointly generate occupancies, atomic coordinates, and lattice parameters in an unsupervised manner, thereby unifying the treatment of diverse disorder types. Evaluated on the COD and MPDS benchmarks, the proposed approach achieves state-of-the-art performance, significantly outperforming adapted ordered-crystal generative models. Notably, it enables the precise recovery of complex chemical disorder patterns and locally sparse structural features.

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.

Problem

• disordered crystal structure prediction
• site-level annotations
• occupancy distribution matrix
• generative models
• formula-conditioned

Innovation

• Disordered Crystal Structure Prediction
• Occupancy Distribution Matrix
• Entropic Polytope Flow
• Flow Matching
• Sinkhorn Inverse Map