Stiefel Flow Matching for Moment-Constrained Structure Elucidation
Keywords: 3D molecular generative models, flow matching, Stiefel manifold, structure elucidation
TL;DR: We propose Stiefel flow matching as a generative model on the Stiefel manifold, which we identify as the space of moment-constrained molecular structures relevant to real-world molecular structure identification.
Abstract: Molecular structure elucidation is a critical step in understanding chemical phenomena, with applications to identifying molecules in natural products, lab syntheses, forensic samples, and the interstellar medium.
We consider the task of elucidating a molecule's 3D structure from only its molecular formula and moments of inertia, motivated by the ability of rotational spectroscopy to precisely measure these moments.
While existing generative models can conditionally sample 3D structures with approximately correct moments, this soft conditioning fails to leverage the many digits of precision afforded by experimental rotational spectroscopy.
To address this, we first show that the space of $n$-atom point clouds with a fixed set of moments of inertia is embedded in the Stiefel manifold $\textrm{St}(n, 4)$.
We then propose Stiefel flow matching as a generative model for elucidating 3D structure under exact moment constraints.
Additionally, we learn simpler and shorter flows by finding approximate solutions for optimal transport on the Stiefel manifold.
Empirically, Stiefel flow matching achieves higher success rates and faster sampling than Euclidean diffusion models, even on high-dimensional manifolds corresponding to large molecules in the GEOM dataset.
Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)
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Submission Number: 13419
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