Symmetry-Informed Geometric Representation for Molecules, Proteins, and
  Crystalline Materials
Shengchao Liu Weitao Du Yanjing Li Zhuoxinran Li Zhiling Zheng Chenru Duan Zhiming Ma Omar Yaghi Anima Anandkumar Christian Borgs Jennifer Chayes Hongyu Guo Jian Tang
Artificial intelligence for scientific discovery has recently generated
significant interest within the machine learning and scientific communities,
particularly in the domains of chemistry, biology, and material discovery. For
these scientific problems, molecules serve as the fundamental building blocks,
and machine learning has emerged as a highly effective and powerful tool for
modeling their geometric structures. Nevertheless, due to the rapidly evolving
process of the field and the knowledge gap between science (e.g., physics,
chemistry, & biology) and machine learning communities, a benchmarking study on
geometrical representation for such data has not been conducted. To address
such an issue, in this paper, we first provide a unified view of the current
symmetry-informed geometric methods, classifying them into three main
categories: invariance, equivariance with spherical frame basis, and
equivariance with vector frame basis. Then we propose a platform, coined
Geom3D, which enables benchmarking the effectiveness of geometric strategies.
Geom3D contains 16 advanced symmetry-informed geometric representation models
and 14 geometric pretraining methods over 46 diverse datasets, including small
molecules, proteins, and crystalline materials. We hope that Geom3D can, on the
one hand, eliminate barriers for machine learning researchers interested in
exploring scientific problems; and, on the other hand, provide valuable
guidance for researchers in computational chemistry, structural biology, and
materials science, aiding in the informed selection of representation
techniques for specific applications.