Riemannian Flow Models with Reinforcement Learning for Molecular Crystal Structure Prediction

Abstract

Crystal structure governs material properties, making crystal structure prediction (CSP) a fundamental problem in materials science. Generative models are a promising approach for solving this problem, but the prevalence of polymorphism, coupled with large unit cells and complex packing geometry, makes the molecular CSP task challenging for existing models. To address this, we introduce Coarse-Grained Open Materials Generation (CG-OMatG), an equivariant Riemannian flow-based generative model. CG-OMatG predicts molecular crystal structures \textit{via} a coarse-grained, hierarchical representation. CG-OMatG treats molecules as rigid bodies---performing both inter- and intra-molecular message passing to construct a geometric representation for molecular packings---and learns to reconstruct molecule centroid positions, orientations, and lattice parameters, conditioned on chemical species and conformer geometry. We train the model on subsets of the Open Molecular Crystals (OMC25) and Cambridge Structural Database (CSD) datasets. Further, we fine-tune the model \textit{via} policy gradient reinforcement learning to steer the model towards generating low-energy candidate structures. We validate the generated structures on the CSP blind test benchmark, assessing agreement with experimentally determined crystals using COMPACK packing-similarity analysis. CG-OMatG exhibits strong performance for generative molecular crystal structure prediction, paving the way for accelerated polymorph screening and organic solid-state materials discovery.

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BibTeX RIS

BibTeX

@misc{egg2026riemannian,
  title = {{Riemannian Flow Models with Reinforcement Learning for Molecular Crystal Structure Prediction}},
  author = {Thomas Egg and Harry Winston Sullivan and Maya M. Martirossyan and Philipp Höllmer and Cheng Zeng and Adrian Roitberg and Mingjie Liu and Richard Hennig and Sapna Sarupria and Ellad B. Tadmor and Stefano Martiniani},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.39773},
  eprint = {2609.39773},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.39773},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Riemannian Flow Models with Reinforcement Learning for Molecular Crystal Structure Prediction
AU  - Thomas Egg
AU  - Harry Winston Sullivan
AU  - Maya M. Martirossyan
AU  - Philipp Höllmer
AU  - Cheng Zeng
AU  - Adrian Roitberg
AU  - Mingjie Liu
AU  - Richard Hennig
AU  - Sapna Sarupria
AU  - Ellad B. Tadmor
AU  - Stefano Martiniani
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.39773
UR  - https://arxiv.org/abs/2609.39773
AB  - Crystal structure governs material properties, making crystal structure prediction (CSP) a fundamental problem in materials science. Generative models are a promising approach for solving this problem, but the prevalence of polymorphism, coupled with large unit cells and complex packing geometry, makes the molecular CSP task challenging for existing models. To address this, we introduce Coarse-Grained Open Materials Generation (CG-OMatG), an equivariant Riemannian flow-based generative model. CG-OMatG predicts molecular crystal structures \textit{via} a coarse-grained, hierarchical representation. CG-OMatG treats molecules as rigid bodies---performing both inter- and intra-molecular message passing to construct a geometric representation for molecular packings---and learns to reconstruct molecule centroid positions, orientations, and lattice parameters, conditioned on chemical species and conformer geometry. We train the model on subsets of the Open Molecular Crystals (OMC25) and Cambridge Structural Database (CSD) datasets. Further, we fine-tune the model \textit{via} policy gradient reinforcement learning to steer the model towards generating low-energy candidate structures. We validate the generated structures on the CSP blind test benchmark, assessing agreement with experimentally determined crystals using COMPACK packing-similarity analysis. CG-OMatG exhibits strong performance for generative molecular crystal structure prediction, paving the way for accelerated polymorph screening and organic solid-state materials discovery.
ER  -

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