Space Group Conditional Flow Matching

• URL: http://arxiv.org/abs/2509.23822v1
• Date: Sun, 28 Sep 2025 11:51:29 GMT
• Title: Space Group Conditional Flow Matching
• Authors: Omri Puny, Yaron Lipman, Benjamin Kurt Miller,
• Abstract summary: Inorganic crystals are periodic, highly-symmetric arrangements of atoms in three-dimensional space.<n>Most generative models that predict atomic coordinates overlook these symmetry constraints.<n>We introduce Space Group Conditional Matching Flow, a novel generative framework that samples significantly closer to the target population of highly-symmetric, stable crystals.
• Score: 24.57489567024265
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Inorganic crystals are periodic, highly-symmetric arrangements of atoms in three-dimensional space. Their structures are constrained by the symmetry operations of a crystallographic \emph{space group} and restricted to lie in specific affine subspaces known as \emph{Wyckoff positions}. The frequency an atom appears in the crystal and its rough positioning are determined by its Wyckoff position. Most generative models that predict atomic coordinates overlook these symmetry constraints, leading to unrealistically high populations of proposed crystals exhibiting limited symmetry. We introduce Space Group Conditional Flow Matching, a novel generative framework that samples significantly closer to the target population of highly-symmetric, stable crystals. We achieve this by conditioning the entire generation process on a given space group and set of Wyckoff positions; specifically, we define a conditionally symmetric noise base distribution and a group-conditioned, equivariant, parametric vector field that restricts the motion of atoms to their initial Wyckoff position. Our form of group-conditioned equivariance is achieved using an efficient reformulation of \emph{group averaging} tailored for symmetric crystals. Importantly, it reduces the computational overhead of symmetrization to a negligible level. We achieve state of the art results on crystal structure prediction and de novo generation benchmarks. We also perform relevant ablations.

Related papers

• Topological crystals and soliton lattices in a Gross-Neveu model with Hilbert-space fragmentation [41.94295877935867]
  We explore the finite-density phase diagram of the single-flavour Gross-Neveu-Wilson (GNW) model.<n>We find a sequence of inhomogeneous ground states that arise through a real-space version of the mechanism of Hilbert-space fragmentation.
  arXiv  Detail & Related papers  (2025-06-23T14:19:35Z)
• Space Group Equivariant Crystal Diffusion [9.03515915097047]
  3D crystals are invariant to discrete groups of isometries called the space groups.<n>We propose SGEquiDiff, a crystal generative model which naturally handles space group constraints.<n> SGEquiDiff achieves state-of-the-art performance on standard benchmark datasets.
  arXiv  Detail & Related papers  (2025-05-16T08:45:04Z)
• Wyckoff Transformer: Generation of Symmetric Crystals [0.5968063252533801]
  Internal symmetry plays a fundamental role in determining physical, chemical, and electronic properties.<n>We introduce WyFormer, a generative model that conditioning on space group symmetry.<n>It achieves this by using Wyckoff positions as the basis for an elegant, compressed, and discrete structure representation.
  arXiv  Detail & Related papers  (2025-03-04T08:50:10Z)
• WyckoffDiff -- A Generative Diffusion Model for Crystal Symmetry [10.980666029958932]
  We propose a generative model, Wyckoff Diffusion, which generates symmetry-based descriptions of crystals.<n>In addition to respecting symmetry by construction, the discrete nature of our model enables fast generation.<n>As a proof-of-concept study, we use WyckoffDiff to find new materials below the convex hull of thermodynamical stability.
  arXiv  Detail & Related papers  (2025-02-10T14:04:23Z)
• SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Models [20.39521603857931]
  We propose SymmCD, a novel diffusion-based generative model that explicitly incorporates crystallographic symmetry into the generative process.<n>We showcase the competitive performance of SymmCD on a subset of the Materials Project, obtaining diverse and valid crystals with realistic symmetries and predicted properties.
  arXiv  Detail & Related papers  (2025-02-05T21:48:48Z)
• CrystalGRW: Generative Modeling of Crystal Structures with Targeted Properties via Geodesic Random Walks [1.2141052067494946]
  We introduce CrystalGRW, a diffusion-based generative model that can predict stable phases validated by density functional theory.<n>CrystalGRW demonstrates the ability to generate realistic crystal structures that are close to their ground states with accuracy comparable to existing models.<n>These features help accelerate materials discovery and inverse design by offering stable, symmetry-consistent crystal candidates for experimental validation.
  arXiv  Detail & Related papers  (2025-01-15T18:26:35Z)
• Topological nature of edge states for one-dimensional systems without symmetry protection [46.87902365052209]
  We numerically verify and analytically prove a winding number invariant that correctly predicts the number of edge states in one-dimensional, nearest-neighbor (between unit cells)<n>Our winding number is invariant under unitary or similarity transforms.
  arXiv  Detail & Related papers  (2024-12-13T19:44:54Z)
• A Space Group Symmetry Informed Network for O(3) Equivariant Crystal Tensor Prediction [89.38877696273364]
  We consider the prediction of general tensor properties of crystalline materials. We propose a General Materials Network (GMTNet), which is carefully designed to satisfy the required symmetries. Experimental results show that our GMTNet achieves promising performance on crystal tensors of various orders.
  arXiv  Detail & Related papers  (2024-06-03T16:26:16Z)
• Complete and Efficient Graph Transformers for Crystal Material Property Prediction [53.32754046881189]
  Crystal structures are characterized by atomic bases within a primitive unit cell that repeats along a regular lattice throughout 3D space. We introduce a novel approach that utilizes the periodic patterns of unit cells to establish the lattice-based representation for each atom. We propose ComFormer, a SE(3) transformer designed specifically for crystalline materials.
  arXiv  Detail & Related papers  (2024-03-18T15:06:37Z)
• Symmetry-restricted quantum circuits are still well-behaved [45.89137831674385]
  We show that quantum circuits restricted by a symmetry inherit the properties of the whole special unitary group $SU(2n)$. It extends prior work on symmetric states to the operators and shows that the operator space follows the same structure as the state space.
  arXiv  Detail & Related papers  (2024-02-26T06:23:39Z)
• Geometric Neural Diffusion Processes [55.891428654434634]
  We extend the framework of diffusion models to incorporate a series of geometric priors in infinite-dimension modelling. We show that with these conditions, the generative functional model admits the same symmetry.
  arXiv  Detail & Related papers  (2023-07-11T16:51:38Z)
• Simulating scalar field theories on quantum computers with limited resources [62.997667081978825]
  We present a quantum algorithm for implementing $phi4$ lattice scalar field theory on qubit computers. The algorithm allows efficient $phi4$ state preparation for a large range of input parameters in both the normal and broken symmetry phases.
  arXiv  Detail & Related papers  (2022-10-14T17:28:15Z)
• Noise-resilient Edge Modes on a Chain of Superconducting Qubits [103.93329374521808]
  Inherent symmetry of a quantum system may protect its otherwise fragile states. We implement the one-dimensional kicked Ising model which exhibits non-local Majorana edge modes (MEMs) with $mathbbZ$ parity symmetry. MEMs are found to be resilient against certain symmetry-breaking noise owing to a prethermalization mechanism.
  arXiv  Detail & Related papers  (2022-04-24T22:34:15Z)
• Quantum anomalous Hall phase in synthetic bilayers via twistless twistronics [58.720142291102135]
  We propose quantum simulators of "twistronic-like" physics based on ultracold atoms and syntheticdimensions. We show that our system exhibits topologicalband structures under appropriate conditions.
  arXiv  Detail & Related papers  (2020-08-06T19:58:05Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.