FlowMM: Generating Materials with Riemannian Flow Matching (2406.04713v1)

Abstract: Crystalline materials are a fundamental component in next-generation technologies, yet modeling their distribution presents unique computational challenges. Of the plausible arrangements of atoms in a periodic lattice only a vanishingly small percentage are thermodynamically stable, which is a key indicator of the materials that can be experimentally realized. Two fundamental tasks in this area are to (a) predict the stable crystal structure of a known composition of elements and (b) propose novel compositions along with their stable structures. We present FlowMM, a pair of generative models that achieve state-of-the-art performance on both tasks while being more efficient and more flexible than competing methods. We generalize Riemannian Flow Matching to suit the symmetries inherent to crystals: translation, rotation, permutation, and periodic boundary conditions. Our framework enables the freedom to choose the flow base distributions, drastically simplifying the problem of learning crystal structures compared with diffusion models. In addition to standard benchmarks, we validate FlowMM's generated structures with quantum chemistry calculations, demonstrating that it is about 3x more efficient, in terms of integration steps, at finding stable materials compared to previous open methods.

• The paper introduces FlowMM, a generative model that leverages Riemannian Flow Matching to efficiently predict stable crystal structures and generate novel compositions.
• The methodology incorporates symmetry-aware geodesic paths and flexible base distributions to enhance accuracy in both crystal structure prediction and de novo generation tasks.
• Experimental results demonstrate a threefold improvement in efficiency, significantly reducing computational cost and integration steps in material generation.

FlowMM: Generating Materials with Riemannian Flow Matching

The task of generating crystalline materials, essential for advancements in next-generation technologies, presents unique computational challenges due to the combinatorial nature of plausible atomic arrangements and their thermodynamic stability constraints. The paper introduces FlowMM, a generative model designed to address the complexities associated with crystalline materials. FlowMM leverages Riemannian Flow Matching to generate crystal structures that are both efficient and flexible compared to traditional methods.

Problem Statement and Paper Contribution

The paper delineates two fundamental tasks in the domain of material science:

1. Crystal Structure Prediction (CSP): Predicting the stable crystal structure of a given elemental composition.
2. De Novo Generation (DNG): Generating novel compositions along with their stable structures.

FlowMM is notable for generalizing Riemannian Flow Matching to accommodate the inherent symmetries of crystalline structures, such as translation, rotation, permutation, and periodic boundary conditions. This generalization enables FlowMM to optimize the generation of crystal structures efficiently.

Methodological Innovations

The primary innovation in FlowMM is the adaptation of Riemannian Flow Matching to the geometric and symmetric properties of crystals. Traditional diffusion models have limitations when dealing with the structured variables in crystals, necessitating different frameworks for various variables. FlowMM addresses these limitations by allowing freedom in the choice of flow base distributions, simplifying the problem compared to diffusion models.

Key methodological contributions include:

• Symmetry-aware Geodesic Paths: These paths preserve the geometrical and symmetry properties of crystal structures during the generative process.
• Flexible Base Distributions: FlowMM permits more natural base distributions, improving the fitting process for lattice parameters.
• Binary Representation for Atom Types: For DNG, a binary representation for atom types reduces dimensionality significantly, thus enhancing the model’s accuracy in predicting the number of unique elements per unit cell.

Numerical Results and Validation

FlowMM demonstrates exceptional performance on standard benchmarks and goes further by validating generated crystal structures through quantum chemistry calculations. It shows approximately a threefold improvement in efficiency—measured in terms of integration steps—over previous open methods for finding stable materials.

Experimental results for CSP and DNG highlight FlowMM's superior performance with respect to both standard proxy metrics and new metrics that estimate thermodynamic stability via expensive quantum chemistry calculations. The results indicate:

• Higher match rates and lower Root-Mean-Square Error (RMSE) in predicting crystal structures compared to competing methods.
• More efficient and accurate generation of stable materials in the DNG task.

Practical and Theoretical Implications

The practical implications of FlowMM are profound in material science and technological applications. By enhancing the efficiency and accuracy of material generation:

• FlowMM accelerates the discovery of new materials that are pivotal in energy storage, carbon capture, and electronics.
• The significant reduction in computational cost and integration steps facilitates more extensive and rapid exploration of the material space.

Theoretically, FlowMM sets a precedent for applying Riemannian Flow Matching to other domains requiring symmetric and structured generative processes. Future developments might explore extending this methodology to other forms of structured data beyond material science, leveraging FlowMM's ability to handle complex symmetries and geometries.

Conclusion

FlowMM represents a significant step forward in the generative modeling of crystalline structures, offering a more efficient and flexible approach compared to previous methodologies. By effectively marrying geometric symmetries with advanced flow matching techniques, FlowMM not only achieves state-of-the-art performance but also opens new avenues for future research in material science and beyond. The model’s ability to generate stable and novel materials efficiently has practical implications that could catalyze further technological advancements.