MOFFlow: Flow Matching for Structure Prediction of Metal-Organic Frameworks

TL;DR

MOFFlow introduces a building-block based, SE(3)-invariant deep generative model for MOF structure prediction using Riemannian flow matching to predict block roto-translations and lattice parameters. By representing MOFs as rigid blocks and operating in $SE(3)$, it dramatically reduces the search space and scales to unit cells with hundreds to thousands of atoms, outperforming traditional CSP and diffusion-based baselines in both accuracy and speed. The framework enforces crystal symmetries, employs a hierarchical MOF-specific architecture with MOFAttention, and demonstrates superior performance on a large MOF dataset, including accurate property reproduction. These results suggest MOFFlow's potential to accelerate MOF discovery and design by enabling scalable, accurate structure generation and property prediction.

Abstract

Metal-organic frameworks (MOFs) are a class of crystalline materials with promising applications in many areas such as carbon capture and drug delivery. In this work, we introduce MOFFlow, the first deep generative model tailored for MOF structure prediction. Existing approaches, including ab initio calculations and even deep generative models, struggle with the complexity of MOF structures due to the large number of atoms in the unit cells. To address this limitation, we propose a novel Riemannian flow matching framework that reduces the dimensionality of the problem by treating the metal nodes and organic linkers as rigid bodies, capitalizing on the inherent modularity of MOFs. By operating in the $SE(3)$ space, MOFFlow effectively captures the roto-translational dynamics of these rigid components in a scalable way. Our experiment demonstrates that MOFFlow accurately predicts MOF structures containing several hundred atoms, significantly outperforming conventional methods and state-of-the-art machine learning baselines while being much faster.

Figures (8)

• Figure 1: Overview of MOFFlow.MOFFlow is a continuous normalizing flow that exploits the modular nature of MOFs by modeling the building blocks (i.e., metal nodes and organic linkers) as rigid bodies. It learns the vector fields for rotation ($\bm{q}$), translation ($\bm{\tau}$), and the lattice ($\bm{\ell}$) that assembles the building blocks into a complete MOF structure.
• Figure 2: Inference trajectory of MOFFlow. Visualization of the inference trajectory of MOFFlow from $t=0$ to $t=1$, showing the progressive assembly of building blocks. We wrap building block centroids inside the lattice for visual clarity.
• Figure 3: Overview of our neural network architecture. Our architecture follows a hierarchical structure, starting with atom-level update layers that encode building block representations into atomic-resolution embeddings. These are followed by block-level update layers, which iteratively refine the roto-translations $(\bm{q}, \bm{\tau})$, block features $\bm{H}$, pairwise features $\bm{Z}$, and lattice parameters $\bm{\ell}$. The final output is a prediction of the clean data $(\hat{\bm{q}}_1, \hat{\bm{\tau}}_1, \hat{\bm{\ell}}_1)$.
• Figure 4: Visualization of the predicted MOF structures. We select structures from the 20 candidates with the lowest RMSE. The lattice is scaled to reflect the relative sizes. MOFFlow accurately generates high-quality predictions with accurate atomic positions and lattice configuration.
• Figure 5: Property distributions. We compare the distributions of key MOF properties for ground-truth, MOFFlow, and DiffCSP. The distributions are histograms smoothed by kernel density estimation. Property units are displayed in the top-right corner of each plot. MOFFlow (red) closely aligns with the ground-truth distribution (blue), while DiffCSP (yellow) shows noticeable deviations. These results highlight that MOFFlow's ability to accurately capture essential MOF properties.