Learning representations through deep generative modeling is a powerful approach for dynamical modeling to discover the most simplified and compressed underlying description of the data, to then use it for other tasks such as prediction. Most learning tasks have intrinsic symmetries, i.e., the input transformations leave the output unchanged, or the output undergoes a similar transformation. The learning process is, however, usually uninformed of these symmetries. Therefore, the learned representations for individually transformed inputs may not be meaningfully related. In this paper, we propose an SO(3) equivariant deep dynamical model (EqDDM) for motion prediction that learns a structured representation of the input space in the sense that the embedding varies with symmetry transformations. EqDDM is equipped with equivariant networks to parameterize the state-space emission and transition models. We demonstrate the superior predictive performance of the proposed model on various motion data.
PETIMOT: A Novel Framework for Inferring Protein Motions from Sparse Data Using SE(3)-Equivariant Graph Neural Networks
Department of Computational, Quantitative, and Synthetic Biology (CQSB), UMR 7238 IBPS, Sorbonne Université, CNRS（索邦大学国家科学研究中心计算、定量与合成生物学系（CQSB），UMR 7238 IBPS）；Univ. Grenoble Alpes, CNRS, Grenoble INP, LJK（格勒诺布尔阿尔卑斯大学国家科学研究中心格勒诺布尔国立理工学院让·库尔实验室（LJK））；Institut universitaire de France (IUF)（法国大学研究院（IUF））
Equivariant Neural Simulators for Stochastic Spatiotemporal Dynamics
Data and Artificial Intelligence Cluster, Eindhoven University of Technology（埃因霍温理工大学数据与人工智能集群）；Swiss Plasma Center, École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院瑞士等离子体中心）
Equivariant geometric convolutions for emulation of dynamical systems
Johns Hopkins University（约翰斯·霍普金斯大学）；New York University（纽约大学）；Max-Planck-Institut für Astronomie（马克斯·普朗克天文研究所）；Flatiron Institute（弗拉蒂伦研究所）；Universidad Autónoma de Madrid（马德里自治大学）；Mathematical Institute for Data Science, Johns Hopkins University（约翰斯·霍普金斯大学数据科学数学研究所）
Heidelberg Institute for Theoretical Studies（海德堡理论研究所）；Mathematical Institute, University of Oxford（牛津大学数学研究所）；City University of Hong Kong（香港城市大学）；IAR, Karlsruhe Institute of Technology（卡尔斯鲁厄技术大学IAR研究所）；Department of Psychiatry, Warneford Hospital（沃内福德医院精神病科）
GDEGAN: Gaussian Dynamic Equivariant Graph Attention Network for Ligand Binding Site Prediction
Department of Artificial Intelligence, Indian Institute of Technology, Kharagpur, India（人工智能系，印度理工学院，Khargpur，印度）；Department of Computer Science, Indian Institute of Technology, Kharagpur, India（计算机科学系，印度理工学院，Khargpur，印度）
