5 papers
Physics-informed Diffusion Generative Model for Time-Series Data Synthesis in Dynamic Systems
Haiteng Wang, Yunfei Zhu, Tao Wang +4
Industrial time-series signals, such as turbine temperature and rotational speed in aero-engines, are essential for monitoring the health and operational status of complex dynamica…
Explicit Discovery of Nonlinear Symmetries from Dynamic Data
Lexiang Hu, Yikang Li, Zhouchen Lin
Symmetry is widely applied in problems such as the design of equivariant networks and the discovery of governing equations, but in complex scenarios, it is not known in advance. Mo…
High-Rank Irreducible Cartesian Tensor Decomposition and Bases of Equivariant Spaces
Shihao Shao, Yikang Li, Zhouchen Lin +1
Irreducible Cartesian tensors (ICTs) play a crucial role in the design of equivariant graph neural networks, as well as in theoretical chemistry and chemical physics. Meanwhile, th…
Governing Equation Discovery from Data Based on Differential Invariants
Lexiang Hu, Yikang Li, Zhouchen Lin
The explicit governing equation is one of the simplest and most intuitive forms for characterizing physical laws. However, directly discovering partial differential equations (PDEs…
Symmetry Discovery for Different Data Types
Lexiang Hu, Yikang Li, Zhouchen Lin
Equivariant neural networks incorporate symmetries into their architecture, achieving higher generalization performance. However, constructing equivariant neural networks typically…