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EP-Flow: Disordered Crystal Structure Prediction without Site-level Annotation

NeurIPS 2026 · Probabilistic and scientific modeling › Molecules and proteins · approach: Flow matching generative modeling

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Proposes EP-Flow, a marginal-constrained flow matching model that generates occupancy distribution matrices, fractional coordinates, and lattice parameters for formula-conditioned disordered crystal structure prediction without site-level annotations.

Problem

Crystal structure prediction for intrinsically disordered materials (substitutional mixing, vacancies, interstitials) when only the chemical formula is given and no site-level disorder annotations are available.

Approach

Represents disordered crystals as occupancy distribution matrices lying on a formula-dependent transportation polytope, canonicalizes them into a shared double-centered zero-marginal space via log-domain double centering, learns a marginal-preserving flow there, and recovers valid occupancies with a Sinkhorn projection.

Key results

• On MPDS Sub-20, EP-Flow reaches 60.82% match rate vs 45.17% for adapted DMFlow, with OccMAE 0.0075 and validity 97.8%.
• On COD Sub-20, EP-Flow reaches 45.39% match rate vs 21.61% for adapted DMFlow.
• Across all eight COD/MPDS subsets, EP-Flow match rate ranges 17.10%-60.82%, outperforming the strongest baseline DMFlow by 7.36-23.78 points.

Surprising findings

• Adapted FlowMM achieves high validity (e.g., 95.90% on MPDS Disorder-20) despite only 0.24% match rate, showing validity does not imply correct structure recovery.
• Removing the Sinkhorn projection and double centering together drops match rate to 0%, while removing only projection keeps 15.78% but raises OccMAE sharply to 0.1277.

Limitations

• Validity on several subsets (e.g., Disorder-50 COD 77.70%, MPDS Sub-50 91.90%) and RMSD lag some baselines, with RMSD computed only over matched samples.
• Benchmarks are self-constructed since no public disordered-occupancy benchmark existed; comparison is against adapted rather than native disordered baselines.
• Physical analogies (Boltzmann, thermodynamic annealing) are heuristic and not formally derived.

Experimental setup

Datasets: COD MPDS

Benchmarks: COD disordered CSP subsets MPDS disordered CSP subsets

Metrics: Match Rate RMSD OccMAE Validity

Baselines: FlowMM OMatG DMFlow

Builds on: FlowMM DMFlow OMatG Riemannian flow matching

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