CrystalGRW: Generative Modeling of Crystal Structures with Targeted Properties via Geodesic Random Walks (2501.08998v2)

Abstract: Determining whether a candidate crystalline material is thermodynamically stable depends on identifying its true ground-state structure, a central challenge in computational materials science. We introduce CrystalGRW, a diffusion-based generative model on Riemannian manifolds that proposes novel crystal configurations and can predict stable phases validated by density functional theory. The crystal properties, such as fractional coordinates, atomic types, and lattice matrices, are represented on suitable Riemannian manifolds, ensuring that new predictions generated through the diffusion process preserve the periodicity of crystal structures. We incorporate an equivariant graph neural network to also account for rotational and translational symmetries during the generation process. CrystalGRW demonstrates the ability to generate realistic crystal structures that are close to their ground states with accuracy comparable to existing models, while also enabling conditional control, such as specifying a desired crystallographic point group. These features help accelerate materials discovery and inverse design by offering stable, symmetry-consistent crystal candidates for experimental validation.

• The paper introduces CrystalGRW, a diffusion model on Riemannian manifolds that generates energetically plausible crystal structures using geodesic random walks.
• The paper employs an equivariant graph neural network to incorporate symmetry constraints, achieving 100% structural and 85.4% compositional validity.
• The paper demonstrates inverse design capability by conditionally generating crystals, with around 71% stability and 75% novelty in the produced configurations.

An Expert Overview of "CrystalGRW: Generative Modeling of Crystal Structures with Targeted Properties via Geodesic Random Walks"

In "CrystalGRW: Generative Modeling of Crystal Structures with Targeted Properties via Geodesic Random Walks," the authors introduce a model centered on an innovative method for generating structurally and energetically plausible crystalline materials. The primary challenge in computational materials science lies in determining the ground-state structure within an immense configurational space, which determines material stability. CrystalGRW employs a diffusion-based generative model on Riemannian manifolds, offering a promising approach to efficiently sample novel crystal configurations for further validation using density functional theory (DFT).

Model Architecture and Methodology

The paper presents CrystalGRW, which operates on Riemannian manifolds, preserving the periodic symmetries inherent in crystal structures. The model represents fractional coordinates, atomic types, and lattice matrices on manifolds that inherently respect periodicity—a 3D torus for coordinates and atomic types on a simplex, enhancing sampling by reflecting these constraints naturally. The method utilizes geodesic random walks (GRW), which describe the diffusion process in the manifold space, aiding in generating new crystal structures by effectively navigating the energy landscape.

Furthermore, the model incorporates an equivariant graph neural network, EquiformerV2, designed to account for symmetry transformations such as rotations and translations. This choice ensures the generative process respects the physical properties symmetries while enabling layers of control, like specifying crystallographic point group symmetries, thereby offering the ability to tailor generation to desired material properties.

Key Insights and Numerical Performance

The authors effectively highlight that CrystalGRW generates crystal structures close to their ground states with an impressive balance between computational efficiency and accuracy. The performance of the model is quantitatively evaluated using several key metrics:

• Validity: 100% structural validity and 85.40% compositional validity suggest that generated structures are not merely theoretical constructs but potential candidates for real-world synthesis.
• Stability and Novelty: Approximately 71% of generated structures are stable when considering energy above the convex hull (E_hull) below 100 meV/atom, a benchmark for DFT validation. Additionally, it demonstrates a 75% novelty and 86% uniqueness in the generated structures, a critical measure for ensuring that the outputs are not just re-creations from the training data but new configurations.
• Inverse Design Capability: The ability to conditionally generate crystals with specific symmetries demonstrates considerable inverse design potential. This capability is tested and validated across numerous point groups, reflecting a robustness in the model's adaptability to adhering to user-specified requirements.

Practical and Theoretical Implications

The practical implications of CrystalGRW are substantial for materials discovery, particularly in applications requiring new materials with specific crystal geometric properties, like catalysts, semiconductors, and superconductors. Theoretically, employing Riemannian manifolds within generative modeling can be seen as an expanded toolkit for simulating complex systems where non-Euclidean spaces better reflect the natural constraints and symmetries inherent in the problem domain.

Looking forward, this approach suggests promising avenues for future developments in AI-driven materials science. By refining conditional generative capabilities, CrystalGRW could accelerate inverse design processes, making it a pivotal tool for tailoring materials properties rapidly across varied industries. Additionally, further exploration of the interplay between manifold learning and generative models is anticipated to yield broader generalizability to other domains of computational science.