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Crystal-GFN: sampling crystals with desirable properties and constraints (2310.04925v2)

Published 7 Oct 2023 in cs.LG

Abstract: Accelerating material discovery holds the potential to greatly help mitigate the climate crisis. Discovering new solid-state materials such as electrocatalysts, super-ionic conductors or photovoltaic materials can have a crucial impact, for instance, in improving the efficiency of renewable energy production and storage. In this paper, we introduce Crystal-GFN, a generative model of crystal structures that sequentially samples structural properties of crystalline materials, namely the space group, composition and lattice parameters. This domain-inspired approach enables the flexible incorporation of physical and structural hard constraints, as well as the use of any available predictive model of a desired physicochemical property as an objective function. To design stable materials, one must target the candidates with the lowest formation energy. Here, we use as objective the formation energy per atom of a crystal structure predicted by a new proxy machine learning model trained on MatBench. The results demonstrate that Crystal-GFN is able to sample highly diverse crystals with low (median -3.1 eV/atom) predicted formation energy.

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Citations (12)
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Summary

  • The paper introduces Crystal-GFN, a generative model that sequentially samples space group, composition, and lattice parameters to produce stable inorganic crystals.
  • It employs a GFlowNet framework with Beta distributions to adhere to crystallography constraints, ensuring physical realism in the generated structures.
  • Experimental results reveal 95% of structures achieve formation energies below -2 eV/atom within 12 hours on a CPU, showcasing its efficiency and potential in material discovery.

Analysis of "Crystal-GFN: Sampling Crystals with Desirable Properties and Constraints"

The paper "Crystal-GFN: sampling crystals with desirable properties and constraints" introduces Crystal-GFN, a generative model targeting the challenge of generating inorganic crystal structures that adhere to specific properties and constraints. This research contributes to the broader context of rapidly evolving methods in accelerated material discovery, a domain pivotal to advancements in renewable energy solutions.

The model operates by sequentially sampling space group, composition, and lattice parameters of a unit cell, leveraging domain knowledge from crystallography and materials science. This approach not only facilitates the generation of stable crystal structures but also incorporates domain-specific constraints more effectively than models that attempt to learn these constraints implicitly.

Methodological Approach

  • Space Group and Composition Sampling: The paper details the sampling of space groups, composing the horce of crystallography knowledge to introduce a three-dimensional space encompassing crystal-lattice systems, point symmetry, and spatial arrangement. By delineating the sample space in this structured manner, Crystal-GFN allows the integration of rules from the internals of crystallography, such as Wyckoff positions.
  • Lattice Parameters: The method samples these parameters in a continuous space, employing mixtures of Beta distributions to model their range effectively. Constraints emerge from and are aligned with crystallography principles, enforcing geometrical compatibility and enhancing sampling efficiency.
  • GFlowNet Framework: With the use of GFlowNets, the model efficiently samples from potentially high-dimensional distributions, enabling the pursuit of diverse viable crystal structures, a task usually hampered by conventional MCMC methods due to mode complexity in scientific data and generation spaces.

Numerical Results

Remarkably, the empirical evaluation unearths the model's capacity to discover crystal structures with significantly low predicted formation energy. A training duration of 12 hours on a CPU-only setup yields a median formation energy of -3.1 eV/atom, with 95% of sampled structures achieving a predicted energy lower than -2 eV/atom. This highlights Crystal-GFN's aptitude for navigating the compositionally and structurally diverse search space effectively within resource constraints.

Despite operating on reduced subset domains and using predictive proxy models, the results provide pivotal insights:

  • The generative process results in high diversity across sampled space groups, compositions, and lattice parameters.
  • The approach ensures the stability and physical realism of generated structures through explicit domain constraints.

Implications and Future Directions

Practically, the model establishes a foundational tool for accelerating the design and discovery of solid-state materials central to advancements in energy storage and conversion technologies. Theoretically, the successful application of GFlowNet to sequential sampling in the hybrid crystallography space pushes methodological boundaries, suggesting pathways for robust and scalable crystal generation strategies, even with constraints.

Future research directions include model expansions to generate atomic coordinates directly or simulate conditions under broader element sets. Enhancements could also explore multifaceted reward frameworks targeting specific material properties, broadening the applicability of Crystal-GFN in diverse industrial problem settings.

In conclusion, "Crystal-GFN: sampling crystals with desirable properties and constraints" presents an adept and strategically grounded entry into designing generative models that capitalize on crystallography frameworks, offering substantive capacities for material innovation. Such developments appear strategically aligned with broader scientific objectives of sustainable technological advancement.

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