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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…
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…
Incorporating Arbitrary Matrix Group Equivariance into KANs
Lexiang Hu, Yisen Wang, Zhouchen Lin
Kolmogorov-Arnold Networks (KANs) have seen great success in scientific domains thanks to spline activation functions, becoming an alternative to Multi-Layer Perceptrons (MLPs). Ho…