Learning Harmonic Molecular Representations on Riemannian Manifold

Yiqun Wang, Yuning Shen, Shi Chen, Lihao Wang, Fei YE, Hao Zhou

Keywords: Riemannian manifold, molecular surface, harmonic analysis, functional map, binding site prediction, rigid protein docking

TL;DR: We propose a harmonic molecular representation learning framework to achieve multi-resolution molecular encoding on 2D Riemannian manifold.

Abstract: Molecular representation learning plays a crucial role in AI-assisted drug discovery research. Encoding 3D molecular structures through Euclidean neural networks has become the prevailing method in the geometric deep learning community. However, the equivariance constraints and message passing in Euclidean space may limit the network expressive power. In this work, we propose a Harmonic Molecular Representation learning (HMR) framework, which represents a molecule using the Laplace-Beltrami eigenfunctions of the molecular surface. HMR offers a multi-resolution representation of molecular geometric and chemical properties on 2D Riemannian manifold. We also introduce a harmonic message passing method to realize efficient spectral message passing over the surface manifold for better molecular encoding. Our proposed method shows comparable predictive power to current models in small molecule property prediction, and outperforms the state-of-the-art deep learning models for the rigid protein docking challenge, demonstrating its versatility in molecular representation learning.

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